Yes! Resistance bands are awesome! Weighted balls also count - I do crunches while holding a 6 pound ball just above my chest and reverse crunches with it held between my knees, ouch in a good way. You can also get small ones that you can use for any exercise you would use normal hand weights for. I also use weighted gloves when I go for a walk to add some strength training to my cardio.
Anything that builds muscle and makes you stronger counts as strength training. Many people, myself included, also consider things like yoga and pilates to be a type of strength training. On days I have to rake leaves I figure I've done my arm strength training for the day. I've done strength training using a child as my weight, and as a bonus they had fun too. ANYTHING can count, as long as it is a strength building activity.