This thread is going to quickly get too long for much usability, but I'll chip in anyway. First off, I will say that with the possible exceptions of the Hammer of Moradin and the Windwalker, most of the worst offenders do NOT come from FR sources, at least in 3.5. I will assume that you're as 3.5-comp as possible, and thus ignore "old versions" or superseded versions of PrCs. My take (OK PrCs excluded, all WotC sources except for non-FR campaign-specific stuff like KoK):
MULTICLASSING PRCs
Arcane trickster/eldritch knight: Weird. If a player is a multiclassed rog/wiz or ftr/wiz, respectively, these classes become no-brainers and make for a more powerful character of that type. However, IMHO, they do NOT make for a more powerful character than a straight wiz/arcane caster PrC. So this one's up to you. If you don't want every single rog/wiz (ftr/wiz) in your game taking arcane trickster (eldritch knight), you may want to change these classes a bit.
Mystic theurge: Underpowered. REALLY underpowered. Even at Wiz3/Clr3/MT 10, this class is inferior. Keep in mind that an odd-level MT is a corner case anyway; the MT 10 will drop back to two spell levels behind the straight wizard or cleric given one more level.
Spellsword: Generally underpowered (see Arioch28's post), EXCEPT that you do not want to allow players to do a one-level dip into this, or they will do it all the time when building fighter-mages and go Eldritch Knight the rest of the way.
ARCANE CASTER
Archmage: OK, except that you really should put reasonable limits on mastery of shaping and mastery of elements, as they are probably a bit too powerful and/or prone to abuse (shapeable anti-magic fields and never having to worry about energy resistance come to mind).
Celestial mystic (BoED): Overpowered. No class should grant all the abilities it does and full caster progression; the loremaster is nearly as bad, but the extra goodies it gets aren't so combat-oriented. I'd say that this class should maybe be reduced to 7/10 caster progression or have some of the abilities stripped out.
Maho-tsukai (OA): Broken, as, for that matter, are the OA taint rules in general. Simply do not allow these characters as PCs in your game. Even if you use them as NPCs, make sure you control the spell DCs with absolute precision, or your PCs will drop like flies.
Nar demonbinder (Unapproachable East): Messy. I'd disallow this PrC if I were you, because it allows characters to start their spell progression at 4th level, which creates weird breaking points.
Red wizard: The circle magic ability is a bit ooky; a serious powergamer can manipulate the rules in this to boost his caster level and stack on free metamagic feats like crazy. However, it is, IMHO, a less likely abuse than any of the other ones I'll mention here.
Spelldancer (Magic of Faerun): Brokity-broke-broken. There's a reason why this one failed to make it into Players' Guide to Faerun. Do not allow.
I know this list seems short, but the fact is that the real abuse with arcane casters is in the spells, not the PrCs...
DIVINE CASTERS
Radiant servant of Pelor (CD): Yup, overpowered. You lose an average of 10 hp over 10 levels for much better turning and healing plus martial weapon profs? Err... I'd just rule this out and use a modified version of the substantially better Morninglord of Lathander (PGtF) instead.
Eye of Horus (PGtF): This class has the same problems as the RSoP, with the additional insult to injury that it accumulates 1/2 epic bonus feat progression and full epic caster progression!
Dweomerkeeper (CD web enhancement): Oy. To answer Olive, the "deal" with DK is that it grants the ability to cast any of the PC's known spells as a supernatural ability. IOW, no SR, no dispelling, AND no components, including XP. Welcome to the world of free wish. Fortunately, there's an easy way to modify this class: Throw out supernatural spell entirely. The mantle ability is still nice, as is improved metamagic at 10th level.
Fist of Raziel (BoED)/Hospitaler (CD): Balanced high or overpowered; it's a matter of opinion and experience. A straight cleric with one of these PrCs IS a better paladin than the paladin, so to speak; I happen to think that paladins are a bit weak, so I'd probably allow one or both of these classes in my game and just dispense with the core paladin entirely.
Holy Liberator (CD): Closer to overpowered than either of the above, IMHO, because it's a paladin in 10 levels (and REALLY a paladin; you get all the goodies) with an alignment that's compatible with nice things like the bard and barbarian (frenzied berserker with good Will save?). I'd probably disallow.
Apostle of peace (BoED)/ur-priest (CD): Seriously consider just getting rid of these classes entirely, or granting them +1 caster progression; IMHO, it will NOT hurt your game. The Vow feats already grant a caster enough flavor without imparting access to a PrC, and ur-priest can be done better anyway with something like the Athar prestige class in Dragon 287. In the alternative, +1 caster progression is better; classes really shouldn't grant 9 levels of spellcasting over 10 class levels, due to the abuse potential when combined with something like mystic theurge.
Risen Martyr (BoED): Weak. This class simply will never be taken willingly by a sane player. Skip it.
Verdant Lord (MotW): Overpowered when combined with cleric. A cleric loses NOTHING by taking this class except turning ability (eh), and gains good BAB (!) plus the ability to wildshape into a crit-immune plant while wielding his mighty array of weapons and armor. Not good.
Warshaper (CW): This is a bit too good for a druid to take a level dip into. I'd move the morphic body ability up to at least 3rd level.
Windwalker (F&P): Might be balanced, actually. The requirements are pretty murderous, and the only big benefit is good BAB. Is good BAB really worth the loss of a caster level plus a serious skill and feat investment? Dunno.
COMBAT CLASSES
Champion of Gwynharwyf: It's a barbarian with improved DR, spells (which he can cast while raging!), divine grace, and smite evil. Overpowered, IMHO.
Frenzied Berserker (CW): It's just not a good class to allow as a PC, IMHO. Either this guy will be overshadowing all the other folks in the party, or he'll be killing them. Additionally, Deathless Frenzy is just not a very good mechanic; the FB can take ANY amount of damage without dying? Barbarians are rager enough for me.
Hammer of Moradin (PGtF): Just too darn many abilities. I'd consider paring down the abilities (aura of courage, DR, the free Far Shot feat, and stalwart could all go without making the class weaker, IMHO) but otherwise leaving it as is; I don't think anything about the class is intrinsically game-breaking.
Hulking Hurler (CW): Requires the DM to fix the throwing mechanics. It's really too easy (without using the Munchkin... er, Miniatures Handbook) to get a character that deals umpteen d6 damage with a thrown object.
Knight of the Chalice (CW): SOOO much weaker against fiends than a ranger with favored enemy (evil outsider) that it just hurts. Either give 'em some decent abilities or skip the PrC.
Peerless Archer (Silver Marches): The ranged power attack ability of this class (Power Shot, gained at PrC level 3) is really too powerful. If you were to simply remove it, or allow the PA to take a limited, arbitrary attack penalty for bonus damage (say, -1 or -2 for +1 or +2, respectively), it might be OK. Otherwise, the class is balanced high but fine, especially in 3.5 where losing out on bonus archery feats is a tough blow.
Runescarred Berserker (Unapproachable East): Barbarians with greater invisibility, heal, righteous might, and spell resistance are just wrong. A mite overpowered.
Singh Rager (OA): From the man who brought you the champion of Gwynharwyf: A lawful "barbarian" (think paladin/samurai synergies here) that gains rage-like abilities (including greater and tireless rages), two good saves, free haste as an (Ex) ability, and the famous full-attack-after-a-charge rush! Plus, you can combine this with the iaijutsu master PrC! This is the reason you do NOT allow OA classes into D&D campaigns...
ROGUE CLASSES
Shadow Thief of Amn (PGtF): I think bonus feats plus sneak attack progression are too much. I also don't think this class is necessary. A straight rogue is just fine to represent its abilities, IMHO.
Telflammar Shadowlord (Unappropachable East): The shadow pounce ability of this class has lent itself to rather wild interpretation. You either need to rework it so that it simply allows dimension door as a swift action or MEA without creating any new actions, or decide that you're dealing with the class differently.