illram, while I don't have BoA, I remember the ads for "Keep the Change". What appealed to me was that all my transactions would be rounded off thus making checkbook balancing easier. I'd rather add $39, $20, $78, and $8 than $38.45, $19.78, $77.23, and $7.98. Plus, yes you set aside the change and they kick in a little at the end. If WF offered it, I'd sign up.
@Mise, when I was younger I definitely was more like how you're describing yourself. Granted, we didn't have debit cards then, so I was still using cash, but I was always obsessed with counting up where each dollar went. So, I'd take out $80 and save all the receipts then reconstruct how I'd spent the money over the course of the next couple weeks (went farther back then!).