I can't really say that I have any "regrets" in this hobby. Usually, if I get outbid on a cel, that's because I either didn't have enough money to buy it, I didn't want it enough, or it went for a ridiculous amount.
Of course, I've been disappointed when I've lost artwork before.
I get over it pretty quickly, though. I don't save images, so I usually even forget!
There are only two major disappointments I can think of, and one minor one. First was a Dilandau cel that went up for auction around Christmas in my first year of collecting. It went for more than I've spent on a cel, even now. Back then, it was a fortune.
Another disappointment came a year or so ago. There was a HxH ending cel up that I wanted desperately. I even talked the seller into shipping internationally (I would have to send the money in yen through the mail). It just ended for too much. A beta member won it, though I haven't seen it in her gallery yet.
A minor one happened a few months ago. There was a smiling Shaoran in his battle costume that was super cute. I kind of wanted it, but I didn't bid, since I was pretty much looking at graduating without a job lined up. It didn't go for an extreme amount of money, and I probably would have been able to purchase him if I had it to spare, but unfortunately, I didn't at the time.
bran-chan wrote:There's been worse
Agreed.
Of course, I'm currently on a break. 
It's on my to-do list. 
But such is life. I just try to think of it as "Well, that's x amount of money I saved today!"
