My two boys have been using knifes in the kitchen to help chop stuff for a while now, both kind of started at the same time as the younger one was copying the older. So the younger was about 4 the older 5, my girl has not expressed any interest in knifes at all. She is 3 at the moment and sees knifes on the table and has no desire to play with them - the boys were very different, from a very early age if a knife was left on a side board or table they'd intentionally go get it [to the point of dragging furniture around to climb up on]- but I wanted to wait till they had a little more control over what they are doing.
None of them have their own knife, I'm going to wait to see if they want one and if they 'need' one before I give them one. I suppose at some point they'll just get one themselves when they are old enough.
I was never given my own knife, I bought my first one on holiday when I was around 8ish - a cheap swiss army knife copy that had loads of tools on but broke pretty quickly - gave up on having a knife, as a child I didn't really have much use for one - I still don't now to be honest.