Amber, you must've been peeking my my "current projects" bag!
I have two shawls that I started with full steam, only to have run out of steam on them. The one, I just decided I'm not thrilled with the pattern or the yarn anymore (peach shawl), and the other one, I'm really not thrilled with the yarn anymore (red shawl). I vowed that I will finish the red shawl for sure, but the peach shawl, I may just tear out what I've already started and return the unused yarn if I can (I bought quite a bit of it) to get something that I really like.
The peach shawl is a shawl I started for somebody when I was not willing to try to "branch out" and do more involved projects, and now that I've been working on more advance stitches, I feel like it looks like a real amateurish attempt, and it was for a very special event, so I think I should just cut my losses and do something really nice.
I guess it just depends on what the project is and why I've put it away as to whether I'll finish it or not. One of my very first projects was for a gift but it was loaded with mistakes, and I didn't know how to correct them, so I put it away until I could figure it out. Later on, I decided it wasn't worth salvaging, so I frogged the whole thing and started over, and I was glad I did, because the FO came out really nice. If it's something my heart isn't in or I get bored with it, I'd say it's likely I won't finish it, although I'm going to try not to do that...I don't want to waste money.