We always did soda cans, or soup cans mostly. Now water bottles or little hugs (the juice drinks) work ok depending on where you're shooting and clean up. My kids are both getting BBguns from their grandparents this year so I'll be subscribing to his thread
I've used Hunts Tomato Paste cans. The little ones. About 3 inches tall and a 1.5 inch diameter. Much harder to hit, enough metal to take hits all day long. Also look for the paper targets with games printed on them. Poker, Billiards, etc. They are much more fun than shooting at plain white paper.
lollipops. Kids old stuff animals. plastic soda 20oz-2L bottles with frozen water inside hanging from a tree branch. old jacket with an old pillow inside. Just any kind of old stuff from the house.
and these. Stick a roll of caps on-end on a relatively hard backing (I used ceiling tiles in my basement firing range) and a square hit made a nice report. At least, with the caps we used to get when I was a kid.