Books I would definitely recommend:
Unearthed Arcana: Very many good variant rules in here, and through it all the only possible broken parts are Flaws (because some aren't well designed to be always punitive for all players, not the basic concept) and LA buyoff (I like the idea, but it is a little unbalanced for LA +1 to effectively change from "-1 character level" to "you lose 3000 xp, only to slowly regain it because of how the xp system gives lower level characters more xp everytime the party hits next level before you").
Complete Warrior, Adventurer, Arcane, and Mage: The first three were all around awesome books with tons of new features and rules. Not just new classes and feats, also little things like new uses for skills (Perform: Weapon Drill, kipping up from prone with a Tumble check, sensing the relative power level of a foe compared to you with Sense Motive, and so on...). Complete Mage introduced cool variant class features and the Reserve feat subsystem.
Tome of Battle: Either love the whole thing to get more interesting or even anime-like fighting classes; or use bits and pieces otherwise. The book has excellent flavor text for everything, and even without the adept base classes, maneuvers are something you might be willing to let PCs gain in small amounts via items or feats for per encounter abilities, a lot of the feats are cool even without maneuvers in existence (Snap Kick to make unarmed combat more viable; Stone Power for people who like to be tanks; the feat to do +1d6 in the first round for those who want a hit hard and early Iajutsu-like character; Evasive Reflexes to use the AoO system to gain more maneuverability in combat, etc...). The Duel of Wills is also an interesting addition to the Intimidate skill.
Magic Item Compendium: MUCH more sensible magic item pricing and body slot rules generally, and gives more fun one use or x times/day items than you may ever get to use -- but you'll want to try. If you have a problem with PCs spending most of their money on static bonuses like ability scores, AC, etc..., this book is definitely for you. It gives noncasters way more stuff to do with their swift/immediate actions, too. For casters, Eternal Wands and Runestaves are interesting new options, especially for not-wizards (Rune Staff most benefits a sorcerer; Eternal Wands let you use any arcane spell that's on them just by being an arcanist, even if it's not on your spell list, which helps classes with limited lists). As an added bonus, it compiles everything from itself and the DMG in treasure tables in the back, and assigns suggested levels for about when it's reasonable to expect a PC to obtain that particular item, for ease of DMing.
Spell Compendium: Lots of interesting new spells in here, and whiel a small % are overpowered, it's no higher a % than are overpowered in the PHB, and generally to a lesser magnitude than say...Shapechange. If you think casters don't need help, you can skip this, but it is a very good book, and a lot of the spells are updated (and in many cases more balanced/nerfed versions) from spells that already appeared in the Complete books.
PHB2: Interesting tactical feats, feats to make a Fighter 20 more viable, good new base classes (I still squirm at the Duskblade's stupidly high spell slots/day and Beguiler's overall toestepping of Rogues despite also being full casters, but overall the classes are solid), a mixed bag of variant class features -- most add to the game, but immediate magic specialist wizard variants range from completely worthless (Evocation's) to compeltely broken and ban-on-sight (Abrupt Jaunt for Conjurors, cause lord knows they needed help!); Decisive Strike is generally worthless, but can be cheesed to be near game-breaking, with generally no happy middle ground between the two in its usages. It also has retraining rules, if you're too dumb to figure out the basic idea of "the player doesn't like his choice, why not let him change it instead of be stuck with it forever" or too stubborn to let him (in the latter case, though, the rules won't matter anyway).
Dungeonscape: Great variant class features, fun new class (Factotum), and pulls double duty as also being a good DM book for designing dungeons and traps.
Eberron Campaign Setting: It's a good setting. Even if you don't want to use the setting, you probably will want to yoink the player races, many of the feats (most aren't campaign-related), and other ideas for your game.
The enivronmental books (Sandstorm, Stormwrack, and Frostburn): Good sources for their respective environments, and has a mix of DM and player material.
Races of the Wild/Destiny/Stone: Overall gives a good amount of flavor text on the PC races, introduces a bunch of great new ones (I love Raptorans, Illumians, and Goliaths), has generally balanced racial feats and variant class levels, and some of my favorite prestige classes.
Books to take pieces from:
Complete Scoundrel: I like skill tricks, the luck feats don't seem well thought out, but do add something new to the game (and definitely aren't broken, at least; weak, quite possibly), and some of the new spells are just fun. I like the one that summons a 5 ft cube of wood. Great to ready to block a charging foe, or to lay out for your own Dungeoncrasher Fighter to slam enemies into if the wall spells are too high level for you!
DMG 2: I like the teamwork benefits concept. A lot.
Book of Exalted Deeds and Book of Vile Darkness: These books simply offer rules and ideas for stuff not covered elsewhere. Vow of Poverty makes choosing to do without sort-of viable. The execution and torture rules in vile darkness are interesting. Just make sure not to let in the broken stuff, like the exalted spells that have great effects at the cost of easily mitigated ability damage, or the Dark Speech feat, which actually allows you to win at D&D. It's in the fine print somewhere.
Dragon Magic: Seems like all the dragon books are chock-full of brokeness (see below). But at least these books have some redeeming portions that might justify gettign them to use.
Books not worth your time / to avoid:
Savage Species: Too much broken garbage in here. I like the racial level progressions idea, but for many races later Races of books covered this anyway, and it's somethnig you as DM could figure out if needed to accomodate a player. Not to mention the progressions they do give are often laughably unbalanced in actual play. Astral Deva gains the ability to Fly ay low levels, but doesn't gain size large until level 19, for example. I must ask you, if you were in a low level game, which do YOU think would be more powerful to have? Mind you, level progressions are the only good thing about the book, and i'm saying even they're broken. Don't even look at the feats and items. The horror, the horror!
Complete Divine and Complete Champion: The former was just a rather "meh" book without much to offer aside from Divine feats (C.Warrior has some, anyway). The latter was just totally never playtested. 1 level dip in Barbarian gives you pounce? Who the hell thought that was ok? Paladin's feat Battle Blessing that makes all their standard action spells swift actions? 1.) Why'd you have to leave the Ranger in the cold like that? 2.) I'd rather just make the Paladin's spell list more useful. Shame to cheat the divine classes out of both of their books, but...Clerics and Druids will probably do just fine without them.
Races of the Dragon: I've never read the whole book, but every single thing I've encountered from it has been broken -- the Wings of Cover and Wings of Flurry Sorcerer spells, the Mighty Wallop and greater version spell; Dragonwrought Kobolds; and more!
Serpent Kingdoms: Also known as "the book that spawned Pun Pun." It also has the Tren, which is a totally broken Alter Self form, a if the spell wasn't strong enough already. But really, that they'd let something so monumentally, utterly wrong as that Sarruhk (spelling) monster is enough to warrant never giving this book a glance.
Monster Manuals 3 and higher: Balance? Who needs balance?