There appear to be four basic situations when it comes to apologies:
1) It's your fault, and you rightfully apologize
2) It's your fault, but you refuse to apologize (pride? anger?)
3) It's not your fault, and you apologize anyway to keep the peace (i.e. you're a middle child like me)
4) It's not your fault, and you refuse to apologize (from your perspective it can seem like you're just being honest - but if the other person feels wronged, I'm sure they have a different opinion!)
I'm pretty good at situations 1 and 2: if something is my fault, then I will almost always apologize. I will also apologize in situation #3, if it's not something I feel strongly about.
However, if it's something I feel strongly about, then I won't apologize in situation #2 if I feel I didn't do something wrong. Of course, if my counterparty feels the same way... then that can be a difficult situation!
Most of the time though, I just apologize. Life is too short to hold onto things. I believe that anger can corrupt and twist you... so I try to let go of it whenever possible.
Is your SO good about apologizing? How about you?