Dogs are easily entertained with a good, cheap game of fetch, which you can do even in the smallest of apartments. Using a toy you already have on-hand, like a rope toy, dog bone, or chew toy, you can add some excitement to your dog's day and keep him entertained for at least 20 minutes. The best thing about this game is that it is very easy to accomplish and doesn't pose any dangers to you, your dog, or your belongings. Just make sure to select the largest room in the apartment, and only throw the toy where it's an open area.
Anytime your dog goes to pick up one toy, say the name of the toy out loud, and touch the toy. For instance, if it's a stuffed shark, call it Jaws. Say "Jaws" and touch the toy. Repeat as necessary. Do it with all the toys, and eventually, when you say a toy's name out-loud, the dog will go find that specific toy and bring it to you. Of course, this takes some time and practice, but it can be a fun thing to do together. Working toward a goal!
It's a great workout, and a lot of fun, without requiring a ton of space to play. It also helps your dog's manners and impulse control. Simply take a lengthy toy, such as a rubberized dog bone, or rope toy, and hold it in your hand. Make sure your dog is in front of you. The tension for the toy should be too much to bear, so eventually the dog will grab the other end of the toy. Keep holding the other end, and let your dog try to take it from you.