I had a ghost shrimp in with one of my bettas, and the betta was so curious about the shrimp! The shrimp went behind the sponge filter, and the betta spent about 10 minutes squeezing himself back there too, so they were both sitting behind the sponge filter. The betta didn't hurt the shrimp, but he just had to see what was going on back there where the shrimp was!
My other betta is so territorial of his java moss "bed". I used to take the moss out for water changes, and the betta would get very upset. When I returned the moss, sometimes he wouldn't wait until I lowered the moss back into place -- he would just swim over and sit on the moss in my hand! Now, thanks to grimlock3000's idea to use a soap dish to rest the moss on, I don't take it out of the tank when I do a water change. I do lower the water level to just about the level of the soap dish and moss. The betta was upset that the water was a little too low for him to get into his bed. He went under the bed, and swam UP through the holes in the soap dish!
(I scooped him out because there really wasn't much water in the dish at that point.) Another time, a bit of food had fallen into the moss, and I reached in to take it out, and the betta bit me! He is very protective of his moss!