I've always been one to 'dwell' on things. This includes behavior that requires forgiveness. Forgiving without an apology is not something i've given much consideration, but i think it usually happens, it just may take time. Often what seems to happen is i forget exactly what the problem is, i just remember that i had a problem with someone. If nothing continues to make me think poorly of that person i just forget about it. I know that has happened on CC. Someone once said some hurtful things and i wrote them off. It's been over a year, i don't remember what they said, only that something was said and i was hurt. We don't interact very much anymore. But whereas before i would've avoided them, now i'm over it. While i would be hesitant to interact with them again on a more personal level, i will still interact with them in forums, etc..
Every so often, though, someone may do something big enough for me to not be able to forget. It then becomes difficult for me to know if i'm just remembering or holding it against them.
Generally, though, an apology will get forgiveness. It may be a little slow at first (depending on the person and situation) but it will happen. But i know years ago, when i was younger, forgiveness wasn't easy to come by. I had a lot more anger and bitterness and been hurt by nearly every friend i'd had. During that time of my life there wasn't a lot of forgiveness going on.
Thinking about this more, as i write it out, i realize how little thought i have given to my ability, or inability, to forgive. One thing i Do know, regardless, is that i do not equate forgiveness to staying around the person. If the behavior is bad enough, then i won't forget and i will act accordingly and distance myself from someone if they show a high enough level of disrespect or insensitivity.