Is an apology worth more if it comes unasked for or if you say that you'd really like one first? Vote away...
An apology is worth more if it comes unbidden -- there's a lot more sincerity behind it then. If you ask for it first, then it's possible it's only being given grudgingly.
Depends on who it is coming from, some peoples apologies carry an overdraft, while others are worth quiet a bit regardless.
apologies given to people who are going to kick your ass if you don't, in my experience, tend to ring hollow- so best say it unasked to compensate
Unasked, definitely. 9 times out of 10 it's sincere. That one time, they know you expect one and give just to feel smug.
it also depends on the situation. even though i'm always sincere in my apologies, i'm not always apologizing for what i did. sometimes, if i don't regret what i did, i can still sincerely apologize to someone because i didn't mean for or want my actions to hurt them, it was just an unfortunate result. othertimes, i realize what i did was wrong, and not just apologize for the results, but apologize for doing it in the first place.