People frequently seem to think that Bards are mechanically weaker than other classes, and I was wondering if this was true?
Not at all; Bards are a very flexible and potent class
At least not if you allow an admittedly-large number of supplements. Even in straight Core, Bards are fairly middle-of-the-road (decidedly better than Fighter, Monk, or Paladin, decidedly worse than Cleric, Druid, or Wizard), though they are quite limited. But if you have a lot of books available, then they have a ton of options out there, many of them quite good.
Inspire Courage is great
Inspire Courage, by default, gives +1 to attack and +1 to damage to all allies who can hear it. Not particularly glamorous, but that’s a pretty sizable bonus. It does, unfortunately, grow very slowly, at +⅛ per level.
Take the Song of the Heart feat (Eberron Campaign Setting), cast inspirational boost (Spell Compendium), activate a Badge of Valor (Magic Item Compendium), and you’re at +4+⅛/level attack & damage. If you’re willing to allow it, Words of Creation (Book of Exalted Deeds) doubles this.
Dragonfire Inspiration (Dragon Magic) allows you to play a separate song that gives +1d6 Fire damage for each +1 to attack/damage your Inspire Courage would normally grant, again to all allies who can hear it. Note that this stacks with Inspire Courage; they’re two separate songs. Now we’re looking at +4 attack, +4d6+4 damage, or twice that with Words of Creation.
Bardic Music can make you a melee powerhouse
Snowflake Wardancing (Frostburn) allows you to add your Charisma to damage rolls, Gauntlet of Heartfelt Blows (Dragon vol. 314) adds Fire damage equal to your Charisma (that’s Charisma×2), and a Crystal Echoblade (Magic Item Compendium) gains bonus Sonic damage if you’re using Bardic Music. The harmonizing magic weapon enhancement (Magic Item Compendium) allows you to attack and use your music together more easily. In combination these can turn a Bard into a very potent melee character, while still distributing considerable bonuses (through the above stuff) to the rest of his party. Use Song of the White Raven (Tome of Battle) to multiclass Bard with Crusader or Warblade for even more martial prowess.
Diplomancy, or just Suggestion
Diplomacy, if you use the rules straight from the book, is absurd. It’s not very hard to make the check necessary to make even your most heated rival fanatical to you (DC 50). Most DMs don’t run Diplomacy this way, and even if you do, a real “diplomancer” quickly becomes dull since everyone is supposed to always do what he wants. Still, never underestimate the power of convincing someone to do what you want.
If you don’t want to rely on Diplomacy, which are probably governed by ill-defined houserules, fascinate and then later suggestion are extremely potent abilities whenever you’ve got to convince a crowd of anything. If you haven’t, read Julius Caesar, Act 3, Scene II (“Friends, Romans, countrymen, lend me your ears”) for just how amazingly awesome this can be. Sure, he used Diplomacy, but the Bard doesn’t even have to.
Don’t underestimate the Bard’s spells: they aren’t a Cleric’s or a Wizard’s, but they’re really quite good. They make a Bard flexible and adaptable.
Some great choices include summon instrument and the aforementioned inspirational boost, as well as grease (see why), glitterdust, heroism, phantom steed, freedom of movement, etc. etc. The various image spells are amazing. Invisibility is never bad. And so on.
Glibness gets its own section. Hell, for that matter, glibness got its very own Order of the Stick comic! This spell is stupid-amazing. +30 to Bluff, on a high-Charisma, high-skill class, means almost nothing that isn’t actively using magical truth-detection abilities is going to fall hook, line, and sinker for even the most preposterous lies. If you cannot think of awesome ways to use this, you’re not trying hard enough.
There are more awesome Bard-related prestige classes than you can shake a stick at. Lyric Thaumaturge (magic+songs), Virtuoso (magic+better songs), Urban Savant (lots of really nice city-themed abilities), Sublime Chord (9th-level spellcasting as a Bard), Warchanter (powerful new songs) etc. etc. The list really does go on. You’ve even got weird things like the Battle Howler of Gruumsh (faster Inspire Courage progression).
Yes and no.
Bards are designed to be flexible; they're a jack-of-all-trades, with an emphasis in being The Face. They have magic - but they're weaker than wizards and clerics. They can have rogue skills - but they're weaker than thieves, because they have multiple important stats and can't just max out dexterity. They can fight - but not as well as fighters or even rogues. And as the bard levels up, those party-wide bonuses start to pale in comparison to having the bard do something other than sing in combat. You can focus in one aspect or another, and get a bard who is great at, say, magic, but they still won't be as powerful in that aspect as, say, a wizard who focuses on magic. But the fact that bards can take almost any role is their prime strength.
If your party lacks a role, then bards can do it - just not quite as well as a character dedicated to filling that role. The trouble with bards in D&D is that the system rewards specialization more than generalization, and bards are generalists. If they're on their own, then they're less likely to be stuck because they can't do something, though they may have problems doing it well.
Bards are The Face
Between bardic knowledge, high social-interaction skills, bardic music, and their sheer reputation, bards are good at persuading people to go their way. People want to be remembered well in bardic songs, and don't want to be vilified by a bard's next original song. Bardic knowledge lets you know what tack to take with people: is the duke insecure about his title? Are those ruins just ruins, or do they have a long history? Bardic knowledge can also short-cut some puzzles or clues, though it won't hand you the quest objective.
Of course, this makes a bard's powers dependent on the GM: if they ignore the (somewhat broken) Diplomacy rules, and don't include any situations where talking will help, and run roughshod over the players' attempts to get information out of an enemy, then all of those bardic powers won't do much; bards won't be very effective in a pure dungeon crawl.
But if your GM likes to include intrigue, skulduggery, persuasion, and talking in the campaign, then a bard far outshines what its mechanical numbers say on the character sheet. A few well-turned phrases at the right moment can end a war or topple a kingdom, and bards are the kings of well-turned phrases.
A single, lone, non-multiclassed bard, is nowhere nearly as powerful as a Wizard, Cleric or Druid, especially in Core (but see below). Still, he is much more versatile than a fighter and it is a property of individual game and individual player if a character/class suffers more from a lack of raw power or from a lack of versatility.
Bard's roles are social, versatility and force multiplier. The first and the second of these are very strong, but depend on the game. The last depends on the composition of allied force - he can add a lot to a field battle, with lots of knights, henchmen, and mounts (more than plus-minus several knights), but not so much to a small band of magic-users who do not rely on melee to fight.
I think a lot of people seriously underestimate the aforementioned "force multiplier" effect.
Plus one to hit and damage, for example (or higher for higher levels), on every single one of your characters using a weapon definitely can add up over the course of a combat. A mass buff, so to speak. The ability to fill any breach at least adequately can be tremendous. Having played several bards, when the cleric goes down ... The bard can heal him, get him back up and running. Not as well as the cleric, but well enough. There is a breach in the frontline? A bard can plug the hole. Not as well as the fighters, but well enough. And so on. A bard is also a good skill monkey, and especially as the levels accumulate, a potential source of information in just about any field that another player isn't already covering.