It depends on the person and situation I think I forgive and forget in the sense of not keep bringing it up most the time, obviously your not going to be able to erase your memory and its natural that something thats happened in the past will effect how you react to a similar situation.
I have had quite a few situations with my Mum where she has been very nasty largely due to her depression but it still hurt and I don't seem able to totally forgive and forget it clouds how I feel about her and what I expect from her I don't have a go at her about it, be funny about it or bring it up and in my heart I know she didn't mean it but its still always there and probably always will be! On the other hand my MIL was extreamly nasty and angry to me when DH and I split up involving another man a couple of years ago it wasn't nice at the time but awhile later when we got back together she appologised to me for it which I didn't feel was necessary I hurt her son, yes theres two sides to every story but her son is hurting shes going to be angry its done and past I appreciate her appology it ment alot but I didn't need it its totally forgiven and forgotten as far as im concerned it has no baring on our relationship now!