How many movies can their possibly be about assassins that lose their memory. Heres a couple off the top of my head. Bourne movies, point of no return, the show Alias, long kiss goodnight.
I don't recall (heh) there being any memory loss in the Killer. I am assuming you are refering to the Chow Yun Fat film. If there is another Killer film, then my mistake. CYF did lose his memory and revert to a child-like state in God of Gamblers, but he wasn't an assassin.
Also La Femme Nikita/Point of No Return/Black Cat had the main character not remembering killing the cop at the begining but that was due to drug use, not amnesia per say. :-)
In some cases, like this movie, it adds character depth... like what could have been if they had not become assissins... in other cases it can use flashbacks to develop the characters with out the need for a formally structured story line..
My favorite is GhostDog, even though he had no memory loss... I like how the flashbacks showed the point of views of both him and Louie (who's life was at stake / where the gun was pointed), and how he lived by the Hagakure (read pg. 172 in the one with the black cover)...
and the final scene was great, along with Leon's in The Professional...
Kind of like "Today I bring death, tomorrow I recieve it"
"America... it is you and I who are perfect, not the next world..." -Ginsberg
The whole niche is that they're "programmed" assasins; programmed to kill and also programmed to forget. The logic behind this is that if the assasin is ever put in a vulnerable position, they won't be able to incriminate any of the major players. Once the completed mission is over, they have to contact their base, for mental maintenance checks.