Yes, it is! It's the single most annoying computer problem I've ever had--and I've had my fair share. Data loss and such may be more devastating, but nothing beats a screwy mouse for the annoyance factor.
Anyway, I have used different mice and experienced the same phenomenon, though not as frequently. It is possible that something with my current mouse is making it happen more often, but at the moment I do not have another one to switch it out with. I'll order one.
However, I have indeed noticed this in the past way back to my first use of Ubuntu, and I have always had the impression that it was not a glitch, but rather a deliberate "feature" that was programmed in to make it possible for people with certain disabilities to drag without holding down the mouse button. It didn't happen all the time (and I couldn't tell how it worked in order to control it, so to me it was unpredictable), but it really did seem like a deliberate thing and not a malfunction. I was sure it was something in the settings that I could turn off, but it never before bothered me quite enough to look up and find out how.
Obviously it has gone haywire now, though (and maybe something in my own mouse is making it more prominent), so getting rid of it has become crucial.
On a side note, Windows 7 has the very same setting, but in their case you have to purposely turn it on--one of the very few things I think they got right.
I think ordering a new mouse may help, but in the meantime, if anyone knows anything about how to turn off the setting that allows this mouse behavior in the first place, please, please tell me.