I used paladins to great effect when I played Warcraft 2, and as anyone who's ever played Warcraft 3 can tell you, paladins were central to the story (Arthas Menethil, better known these days as The Lich King, started out as a Paladin of the Silver Hand under Uther the Lightbringer, the original Paladin). Oddly enough, when I started playing WoW back in June of 2005, my first character wasn't a Paladin (I rolled Horde, and thus couldn't). However, as soon as I started playing as Alliance on a different server, I created one immediately.
Finishing the character creation process, I was filled with excitement -- I had a big two-handed mace, just as the paladins in Warcraft 3 did. A few moments later I was outside of Northshire Abbey and off on my first quest. I hit the trainer, and had high hopes! I was only level 2, and already had Devotion Aura and Holy Light, two abilities pulled directly from Warcraft 3. This could only get better. As I leveled though, I began to wonder, "where are my special attacks?" I had Judgment, sure, but that was a spell. I'd already played a Rogue and a Warrior, so I expected to get some kind of special attack that would do additional damage, as my other characters had. Sadly, my expectations were quickly dashed.
After a small side-trip on the internet to research Paladin abilities, I was distraught. "No special attack? Just spells?" It got worse. More research turned up another disturbing fact: all paladins do in endgame raids is heal. "This can't be right," I thought. "There were better damage dealing heroes in Warcraft 3, but the Paladin was an amazing support character, capable of healing, raising their fallen allies, and enhancing defensive capabilities all while dealing respectable damage." With no special attacks or damage dealing spell (other than Judgment, which doesn't always damage your target), the prospect of leveling up looked grim.
Paladins are the only class in the game with such a distinct disadvantage when it comes to damage dealing (as Zach talked about in detail here). Seal of Righteousness helps early on (as does Seal of Command later, if you go Ret), but neither are true substitutes for a special attack or a harmful spell -- all you've got is auto-attack and Judgment. One could argue that Shaman have a similar handicap, but Shaman have access to Lightning Bolt and Shocks (similar to damage dealing Judgments, but on a shorter cooldown and they all deal damage).
I don't expect a Paladin's melee options to match a Rogue's or even a Warrior's, but auto-attacking and praying for SoC to proc is no way to fight. I'm well aware that Crusader Strike is available (at 50, with talents), and that helps, but it doesn't make up for the fact that the other pure melee classes (rogues and warriors) either start with an instant attack, or get one at least 10 levels earlier than paladins do.
Unfortunately, I can't really think of anything we could get that wouldn't cause our other abilities to go under scrutiny (the last thing we need is a nerf). Adding an instant attack or 'on next attack' special that's available earlier on might be seen as overpowered when combined with Judgment and Seals.
Retribution paladins have come a long way -- well played and well geared ones can put out some great damage and be a viable option to fill a DPS slot in a party or raid, and with the introduction of Patch 2.4, it's likely they'll see another boost due to better itemization.
Protection paladins are some of the finest tanks around (they are my favorite by far, but then again, I'm a bit biased). Their health issue has been addressed, and should be looked at not as an alternative, but as a fine choice for a main tank. Gimmicky fights may be more difficult, but they can tank anything -- a fact which has been proven multiple times now.
Holy paladins are getting a boost to Holy Shock in 2.4, as well as access to a trinket which seems tailor made for Paladin healing (Vial of the Sunwell). A trinket can't truly make up for the lack of instant heals, but between the improved Holy Shock and this trinket, at least there are some options open for instant healing (every 15 seconds / 2 minutes, anyway). The resilience change that lessens the effects of mana burns should help those who like to PvP, since draining a Paladin's mana pool seems to be a popular tactic in arenas. In PvE situations they're as strong as they ever were, but I've never really liked the idea of paladins as a pure healer. I always saw their role being much as it was in Warcraft 3 -- melee combatants who strengthen their allies and are able to heal if necessary. I won't lie, I have healed full time with my Paladin before, but I don't think I could ever go back to it. Protection is too much fun, and is much closer to my vision of the class.
Despite all the problems and hardships I've had with the class, I still love it. I've got high hopes for the future of the class (especially heading into the next expansion... really can't wait to see those expanded talent trees), and I'm excited that the reborn Order of the Silver Hand seems to figure prominently in Wrath of the Lich King. I can't ever imagine a day where I wouldn't want to play my Paladin.