From the core?
Fighter. Even more than paladin.
A paladin could conceivably serve in a pseudo-assassination 'strike at the head and the body dies' capacity. Riding into the heart of the enemy army on his celestial griffon or juvenile gold dragon mount, laying the smite down and then riding back with the head of his foeman, leaving the disorganized evil horde to rethink their evil ways.
The keys to assassination (I see this as meaning 'striking at an important figure directly rather than peripherally, ideally without having to deal with many/any mooks') are speed, stealth and striking power. You can lose one of the three and have a shot at pulling it off, but probably not two and definitely not all three.
Class By Class
Bard loses striking power but has both stealth and speed (via spells). He will have trouble setting up the kill against a powerful opponent; his best bet is probably enchantment followed by subtle poison, or seduction followed by coup de grace. However, a high level bard basically can't be caught or captured by humanoids unless they're extremely powerful, because of his enchantment and illusion abilities.
Barbarian loses stealth (sort of) but has speed (fast movement) and striking power (rage). He's not likely to one-shot a powerful foe, which is a Bad Thing, but he has a better than average chance to survive to get another shot. Nothing says barbarians have to be unsubtle; Conan, on whom the class is (very loosely) based, often snuck up on foes and killed them stealthily.
Cleric is entirely dependent on domains. Clerics can, however, do most anything with the right setup. Obviously a cleric with Healing and Protection is going to be rather poor at this, but one with Trickery and Travel will be quite effective.
Druid pulls it off easily, as with most roles. Wildshape into bird, infiltrate enemy fortress, wildshape into bear, lay down smack, wildshape into rat and creep away. Alternately, he can call lightning or summon nature's allies without ever revealing his location; absolutely brutal to defend against.
Monk has speed and stealth in spades, and can potentially get off a stun lock to make up for low damage. A stun lock *will* kill any single combatant that can't reliably break out of it in. Not to mention the ability of high level monks to kill with a touch, however unreliably.
Paladin loses stealth but has speed (special mount) and striking power (smite evil) in spades. He can strike down an evil foe in one blow if he blows all his power on that blow - and the best part is, if he discovers to his horror that he's been deceived and his target is not evil, he almost certainly won't kill him in the process.
Ranger has stealth, speed, and, since his favored enemy is almost guaranteed to be the type he assassinates, striking power. Like the monk he's ideally suited to traditional assassination.
Rogue is the obvious assassin class, but actually lacks speed compared to ranger (who can simulate it with a ride-able animal companion and/or entangle spells) or, obviously, monk. Sneak attack brings the pain, high skill points and Dex focus bring the stealth. A rogue has to slip in and out unseen to pull it off, though; he can't blitz and escape like, say, a paladin or barbarian 'assassin,' or certainly a druid.
Sorcerer, with the right spell selection, has everything he needs. Of course, a good assassin-sorc won't be a good blaster-sorc or adventurer-sorc, so he has to be dedicated to do it. Being a glass cannon doesn't matter much when you only need one shot, nor does going nova when you're completely proactive.
Wizard is like sorcerer, but with better spell selection and a slightly less devastating nova.
Fighter, though - fighter's got nothing to make him even a passable assassin. He generally can't one-shot a strong opponent because he doesn't have much in the way of limited use, high power attacks like spells, smites or sneak attacks. He can't outrun anyone because he's typically in heavy armor and even when not has no movement abilities. He can't sneak because he doesn't have the spells or skills to do it.
