Amnesia

Ha ha! I don't have to make a backstory for you, GM, because my character has Amnesia!

What a great way for the player to avoid a backstory. What a great way for the GM to get even with him for it!

When making up a backstory for a player who has amnesia, you must consider the source of the amnesia.

Repressed Memories: Something horrible happened to the character and was repressed by the subconscious. Less likely with eiditic memory.
Head Injury: Some head injury happened and removed a bunch of the character's life.
Magic Involvement: Somone has erased the character's memory.
Drug Addiction: The character has lost large parts of his memory of the course of alcoholism or extreme drug use.
Cyberware/Bioware: Certain cyber and bioware inhibits the brain's abilities to make memories, and this could be the cause of amnesia.
Disease: The character could be old or have dementia or some other disease that may cause amnesia.

Each of these carries a certain implication: A head injury implies a terrible accident (or combat), while repressed memories indicate a horrible past. Magic means that someone wanted to keep that past a secret, and Drug addiction means the character was/is an addict. Cyberware would have to be intentional or impanted by a company, and may still be there! And diseases, well, they're trouble on their own!

If the player isn't going to choose a source, you can choose one for him. And therein you've provided your own backstory hook.

Some character's aren't happy with their amnesia backstory. Of course, you can remind them that they were free to create their own backstory (even having chosen amnesia!), and their failure to do that was an invitation for you to make your own. Plus, many sources of amnesia represent a troubled past (memory wipe, repressed memory, drug addiction, implanted cyberware) or a troubled present (disease, drug addiction).

Also, eiditic memory might inhibit disease or drug addiction from being a source, forcing you to go with another (maybe worse) option. Eiditic memory might also prevent repressed memories, forcing memories to be wiped via magic or "accident".

Keep in mind PC's day jobs and other details when making backstories. Police and many other corporate jobs to background checks on characters, so the player would be aware of his past if it was something that would show up on a background check, and if they have the same identity, and accident would show up in medical history, as would existing cyberware (hello mind wipe!).

Sometimes you can be a little too cruel, GM, but this should be an encouragement for a PC to write his own backstory, even if the character has amnesia!