In a Table Top game this is somewhat harder to pull off, simply because the player needs to have their sheet in front of them, and not having their sheet makes it harder for the GM who then not only needs to keep track of all the NPCs, but of that PCs sheet as well. So can it not be done then?
Heck no, it can be done. There are in fact two general ways I have seen it work too. Just, you need to know going in that you are asking the GM for a big favor by doing this, so know that ahead of time and explain it to them. So what are the two ways?
Type 1: Build in Unison
This method of doing things will kill some of the suspense for you out of character, but at the same time makes it more likely that the character you will get is one that you want to play. How it works is quite simple, you talk to the GM about what you want to play (including the amnesiac). You don't necessarily do details or anything, but bring up some things. Like, if you were a Fire Fighter, or Special Forces, or a cop or something, bring it up and see how they like it. Possibly go into some reasons as for why you are an amnesiac. After the conversation, the GM will make the sheet for you, make the final decisions on the character's life and present you with the mostly blank sheet with the information you may already know about your character. Even if it is just a name.
If you just want to play an amnesiac, you can also do everything yourself like any other character, and then just talk to the GM about the fact that you are an amnesiac, what you want that to mean, and what you want to start triggering memories. Afterwards, just play the game. I listed it here, as it is a method of built in unison.
Type 2: GM Built
This is the other way, the GM builds the character for you like any other character. He gives you a back story, NPC connections, story connections, flaws and advantages. You just don't know about them, and have to figure it out as the game goes on. This gives you the player the mystery, as well as the character, but at the cost of potentially having something you don't like. The GM could accidentally hit wrong on what you were looking for, you were looking for a Jason Bourne, and instead you get some sort of psychic, or a thief.
Aside from that though, there isn't all that much to say about type 2.
If it isn't obvious, I prefer the Type 1 to the Type 2. The GM can be more or less involved depending on personal preference, but keeping the player in the loop is vital in my opinion for maintaining fun factor of the game as it goes along. I would rather, as both a player and GM, that some of the mystery on an OOC level was ruined if it meant that the player got the character they wanted to play. After all, a character you can't have fun with just isn't worth it.
So keep this in mind when going for an Amnesiac, and most of all, have fun with it.