The objectives of an Assassin are;
Advertise services.
Locate targets.
Get to protected / secure targets.
Kill targets.
Get out alive, and preferably undetected.
Collect payment without getting killed by unreliable employer.
Most employers will know where their target is (with a few exceptions, like the merchant who tells you to find that no-good elven minstrel who blew through town three months ago and knocked up his daughter...), so step two isn't always gonna be required.
For the majority of these functions, powers that allow one to bypass security and get in / out unseen are key. Rogues with trapfinding and ridiculous stealth numbers, Bards or Beguilers with ridiculous Disguise / Bluff skills who schmooze their way in and then make the kill and use magic to escape, Ninja or Shadow Dancers with the appropriate class abilities, various spellcasters and Warlocks with the right Invocations, Psions.
Ideally, the Assassin kills quickly, quietly and, in a perfect world, with a single blow. Sneak Attack or Sudden Strike are key for one-shot kills, although Death Attack and poison could also help somewhat. A Warlock 'assassin' using Hideous Blow, a Psion overloading some damaging effect, a Soulknife using Deep Impact and Psychic Strike out the wazoo, or a spellcaster using Maximized Twinned Scorching Ray of DOOOM are all variations on this same feature. Big, beeeeeg bang.
The notion that an 'assassin' is some sort of awesome combatant who can hold his own against a dozen armed men (a la various movies) is just completely out of the scope here. The dude who walks through all of your guards, mowing them down, shoots you, and then walks out unmolested isn't an 'assassin,' he's just some ridiculously higher-level character showing off. If the assassin has to fight, he's already screwed up, and 'ninja' fighting consisted of throws and the like, as the assassin's job is to make a clean kill and then get away, not to kill a bunch of armored guards, any one of whom can probably kick his butt in a stand-up fight. (At least in the real-world, where we don't have levels and the bestest 'assassin' in the entire world would die within moments of some servant girl's dagger entering his gut.)