The burnt diode is a unidirectional transient voltage suppressor (it also protects against reversed polarity), and it's on the 5v rail (the other one to the right is on the 12v rail). It shorted out (again, due to voltage peak or being plugged backwards) and it can be removed no problem (it's merely a protection, and it sure did its job here).
The thing is, I'd be seriously worried. The drive itself will most likely work after removing the diode, that's not the concern. The concern is what made this happen? If you plugged it backwards (hey, I've seen it done before), then we have our answer (just don't plug it backwards again!) but otherwise... I'd be VERY worried about the power supply's output (nasty voltage peaks can and will damage anything). In fact, if it was a nasty peak on the 5v rail, chances are that this diode saved your entire computer by shorting... And these things don't typically short like this for no reason.
I'd be doubly worried if it was a no-name generic PSU (even more so now as it had to provide power on a short circuited 5v rail).