The Beguiler is a character class for 3.5 Edition D&D printed in the Players Handbook II.
Its a sort of hybrid caster/rogue in the same way that the Spellthief class is. But just as the Duskblade is to Hexblade (and indicating a trend between PHBII and the Complete... series of books) the Beguiler has much more broad application for a party and fits in more smoothly.
On the first look, Beguilers kind of suck. Terrible BAB (yet despite this proficient in hand crossbow, rapier, shortbow, and short sword for some reason), only a single good save (Will), and pretty weak hit points. They get spellcasting about on par with a sorcerer, but rather than getting to choose spells, they get access to a set list of each spell level. So why in the world would you want one of these guys?
Well, hold up there, chief. First off, they get as many skills as a bard does, both in quantity (6 + Int) and quality (they have all the usual "skill monkey" skills, including the delightful Use Magic Device). Since their spellcasting is Int-based, you're getting good SAD synergy in this class: you do need Charisma, Dexterity and Constitution, but only as much as you can squeeze out once Intelligence is maxed. Since you're probably never going to be a gish, you don't need Strength (at the very least, you need to seek damage output from another source such as sneak attack), and you can pretty much dump Wisdom as well (though watch out if you want to be a scout, since Wisdom affects Listen and Spot).
Secondly, beguiler spellcasting is actually pretty fucking good. True, you don't get to pick any spells, but the ones you get are usually some real bread-and-butter picks. You've got a great mix of social/"face" spells (charm/dominate variants, glibness, suggestion), stealth (most invisibility variants, undetectable alignment, misdirection, nondetection, silence, blur/displacement), and even some really handy divination for scouting (detect secret doors, detect thoughts, clairaudience/clairvoyance, freedom of movement, locate creature, sending). Sure you lack a few little extras, but that's what UMD and some spare magic items are there for. You even get some good situational spells: mage armor and mirror image for defense, and the whelm variants (which do nonlethal damage and are one of the few "offensive" spells to target Will instead of Fort or Ref). And before you think that beguilers are just so much meatbread for a dedicated God-wizard, not so: they do in fact get access to greater dispel magic and time stop, which is nothing any archmage can handwave at the best of times. (Note, I wouldn't try to get into a pissing match with a fully tricked-out wizard or CoDzilla, but hey, a beguiler can hold their own, something sure to make the bastards look twice. Just ready an action for the greater dispel each round and pray to the gods you win your caster level checks.)
Lastly, beguilers get a smattering of secondary abilities that kind of make it worth sticking with them a bit. Armored mage means they can wear light armor, and if you drop a feat for Battle Caster, and find some way to pick up medium armor proficiency, you can take advantage of mithril full plate just like other gishes do. Trapfinding needs no explanation: if the rogue truly wants to sell it off for an ACF, a beguiler has no trouble stepping up to the plate and taking over that role. Cloaked casting isn't entirely worth it... unless you get to beguiler 20, when you actually get to ignore SR, and if you need to have it explained why this is a great thing, you clearly don't play much 3.5. Surprise casting is not bad, but there's no spells in the beguiler list that require attack rolls, but you can in fact get a feint as a swift action eventually, which is even cooler with certain builds. Advanced learning is the clutch ability here: you can slide any enchantment or illusion spell into your list, which automatically means you go right for shadow conjuration and shadow evocation spells at every opportunity, which basically doubles (or more) your available spells. You even get Still Spell and Silent Spell a bit later, because why the fuck not be more stealthy when casting spells?
Making Beguilers Work
By itself, beguiler makes a pretty decent scout/"face" class. The real question in picking between the bard and the beguiler is if you need more party-wide support or more situational support. Bards can boost everything everyone does in combat, and provide backup healing as needed, but they are capped at 6th-level spells and while they are slightly more useful in melee, they'll always really be more of a support class than anything.
Beguiler, by comparison, does very little for the party in terms of buffs or heals, but they can perform a huge variety of situational needs. That's because they can spontaneously cast from a full list of spells at each spell level, a level of variety that even sorcerers lack without items. Granted, sorcerers can use far more wands, staves, and scrolls than a beguiler - all of the wizard/sorcerer spells are on their list, but a beguiler is limited to what was listed in PHB2. The flip side to that is, beguilers have UMD, which allows them to use any items they want if they are good enough on the skill check.
So if you pick beguiler, you're doing it to be very proactive and look for situations where you have the right skills and spells to overcome a challenge without the rest of the party even breaking out into initiative rolls. They aren't exactly a "battlefield" controller, but the beguiler is very good at locking down individual threats in a pretty impressive variety of ways: diplomacy, mindfucking with illusions and enchantments, or just going for a knockout with various abilities.
There is a weakness to beguilers, though: mindless foes like constructs and undead. These guys are immune to your best mind-affecting stuff. That doesn't mean you're totally screwed, though. Against melee-oriented stuff, just use items with UMD to zap them, and against casters help with shutting down their spellcasting. Being mindless may actually render a foe more vulnerable to illusions however, as they can't make basic conclusions like "that wall that just appeared is an illusion" short of actually touching the illusion.
So, you can stick with beguiler 20 and get some mileage out of them. But what if we want to branch out and prestige?
By and far, one of the best options for a beguiler is go with an Unseen Seer build (courtesy of Complete Mage). You should dip rogue 1 to pick up sneak attack that will improve in Unseen Seer, but you can dump trapfinding for a more useful ACF. If the DM will let you take Poison Use from Drow of the Underdark (there's nothing specifically saying those ACFs are "only" for drow), that might be a great tool in the early and mid levels, or see about taking Mimic from Exemplars of Evil for a once/day disguise self (useful in a pinch in several places, if you're creative). If you're playing Eberron, take a changeling rogue as your first level and get a bazillion skill points as well as the amazing abilities of Social Intuition (which makes almost all of your social skill rolls way better/easier). Shit, if your DM lets you play a changeling in other settings, go for it there, too; this one ACF is amazeballs.
Anyway, after that one level of rogue gets you some sneak attack, go full Unseen Seer. Soon as you get advanced learning there, take the spell hunter's eye from PHB2 and enjoy doing unseemly amounts of sneak attack on command. Anything else is pretty much icing on the cake; find divination spells from ranger or assassin lists that help you do more damage, or bypass various kinds of defenses (especially on constructs or undead). Guarded mind is a great ability, but don't forget that mind blank is always a better effect when you can get it.
Oh, as a side note, when you get to arcane caster level 5th, dip Mindbender. Telepathy is always made of win, and it's ten times more important if you're the party "face" or scout. This is especially true if you take the Mindsight (Lords of Madness) feat, which makes that telepathy into blind sense. Beguiler 5/Mindbender 1/Beguiler 14 is considered a solid build in its own right, as the dip delays Advanced Learning so it lets you pick higher level spells.
Finishing out an unseen seer build is a tricky debate. Abjurant Champion is great for the combat-oriented stuff you can do with it, including dispelling enemy spellcasters, buffing your own combat abilities by dumping spell slots, and it even gets semi-decent skills. Arcane Trickster is considered a viable go-to for this build, but you're looking at being more skill monkey and less combat skirmisher (though you do get a couple more sneak attack dice). Fatespinner is very interesting, indeed: it only loses a spellcasting level at the end, so you'll get your 9th-level spells first, and it actually has some very good buffing/debuffing mechanics that could be clutch. Nightmare Spinner looks kind of cool, but mechanically sucks; anything past CR 15 is going to laugh at your attempts to scare it to death, especially undead and constructs you can't hurt that way. Magical Trickster or Uncanny Trickster make good dips, the latter one especially for skill points and bonus skill tricks, but don't mix the two up; pick one or the other, or you'll never get your delicious 9th-level spells.
For feats, you have a few choices available. When you get +3 BAB, take Arcane Strike to help your sneak attack ability more, as well as to help you facing constructs and undead: you can dump spell slots right into melee attack and damage. Draconic Heritage feats open up some additional abilities if your beguiler spells aren't as useful, and being able to do a breath weapon for energy damage is one of the few ways to get such an ability if you don't otherwise have it, plus some of these draconic feats will add to your spell list. Versatile Spellcaster is a great idea, since you can throw more high-level spells with it, vital in fights against enemy spellcasters. Even a feat as simple as Skill Focus (Use Magic Device) can actually be a huge benefit if it means you can never fail a UMD check at a critical moment.
For items, the same flexibility you saw in prestige classes and feats applies here. It is tempting to make a beeline straight for traditional rogue stuff like rapiers, daggers, etc. Fuck that. Instead, you need items that let you pretend to be fifty different things. So what you want is either a custom-made runestaff (Magic Item Compendium), or just get the runestaff of power straight up since it has that awesome smite ability and the +2 luck bonus. Throw in a wand chamber (Dungeonscape) and add a wand of nerveskitter so you can get yourself a +5 bonus to initiative (assuming you make the UMD check), or a wand of wraithstrike to hit incorporeal assholes. Use eternal wands or the regular ones to cover spells you could really use at odd moments or just a few times a day, like prestidigitation, endure elements, unseen servant, etc. If you can afford them, runestaffs are really the best way to burn off spell slots to do more useful things, but you need a way to carry them around, such as an Ehlonna's quiver or a Heward's handy haversack (both of which are more desirable since retrieving the runestaff won't be a hassle or trigger an attack of opportunity).The Rainment of the Four from (Magic Item Compendium) is another option for expanding your casting options, letting you convert spells into Magic Missile, Fireball, Freedom of Movement and Teleport.
The rod of shadowblending from Complete Mage is a godsend: you can convert minor image to shadow conjuration, and major image to shadow evocation. It only works 3 times a day, but it lets you get access to those spells a full level lower than normal. Ring of telekinesis is always good for a variety of purposes. If your DM actually lets you buy a psychoactive skin of Proteus as soon as you can afford it, then get it, because on-demand metamorphosis for 7 minutes at a time is insane. Find a good source of indefinite flight, be it carpet, cloak/wings, or whatever.
If Dragon Compendium is allowed, you qualify for bloodline feats. These give you access to an extra spell of each level at the cost of losing access to certain categories of spell. While a turn off for the Sorcerer they were intended for, your spell list is narrow enough you have few if any of the prohibited spells anyways.
The bottom line, no matter what prestige class, feat, or item you take, the beguiler works best by being able to change things up as the situation develops. Brute force is not always the solution to a situation, and changing the scenario on the DM with various tricks can be more useful than simply annihilating everything with raw power.