Nil Mortifi Sine Lucre
Evil
The other requirement for an assassin, besides killing someone and having the right skills, is that an assassin has to be evil. Simply put, assassins are bastards. It's not just that they kill people. There is more to it than that. Here are a few hints on how the different kinds of assassins might view their work.
Lawful Evil
The lawful evil assassin is cold, calculating and methodical. They do not assassinate their victims without a carefully-worked-out plan. They are diligent, patient and organised. There may be specific rules on the type of assassination the guild allows them to perform -- such rules could determine the weapons they use, the types of poison allowed them, and whether or not they are required to tell the victim who they are, who sent them and why (if applicable) they have been chosen.
It is possible that their work is not illegal -- in a lawful evil society, for example -- in that case assassins are often employees of the state or the church, employed to kill heretics, dissidents or foreigners.
Neutral Evil
The neutral evil assassin is not quite so rigid as his lawful evil counterpart. Is assassination an officially recognised part of urban life? If not, never mind. Sometimes one must take risks for the guild. They may make plans but are able and willing to improvise as the situation demands. The neutral evil assassin may have any reason for doing what he does. While he might feel a sense of duty to the guild, chances are he kills simply because it is the best way to advance himself quickly, and that he rather enjoys it. In many ways the stereotypical assassin is neutral evil; organised but flexible, but undoubtedly evil.
Chaotic Evil
The chaotic evil assassin is a dangerous figure indeed. Uncaring about the illegality of his actions, he may even feel no loyalty towards his guild. Once he has killed his victim, he may loot the corpse or go on a killing spree. Their plans tend to be simple, and any details are almost always changed at the last minute. Chaotic assassins are unpredictable and delight in the hunt, terrifying their quarries before killing them. They stretch their mission parameters as far as they can; if all they are ordered to do is terminate their victim, then they may capture her and torture her to death. Excessive, perhaps, but the mission is accomplished, and one should always try to enjoy one's work! Does the man who hired them have plenty of money? Has he already paid? Fine. Perhaps killing him too would give them access to the rest of his money.
Conclusion
What sort of conclusion can we draw from this? Well, er... not much of one. Not a good idea for a PC class. They make great NPCs. You could base a pretty cool campaign on 'em if one of your players wants to be an assassin, and don't even have to let him become one.
Oh, and if they want to be assassins just because they've read a few Terry Pratchett novels, play GURPS: Discworld instead. At least then they can get what they want.