Pushups are one of the most portable exercises I know–you can do them pretty much anywhere. A good habit to get into is to do a set of pushups right before you get in the shower, every time you shower.
If you concentrate on activating your lats, pushups are a pretty comprehensive upper body workout. They will work your arms, chest, back, core (squeeze your abs!), and even your quads and gluts (squeeze them too!). If you’re doing them everyday, I don’t recommend doing more than 50-100.
This Wikipedia Article on Push-ups has more information than you probably want to know about pushups.
In the picture on the Wikipedia page, the guy demonstrating is not going through a full range of motion. Chest to deck on the bottom, arms fully extended at the top!
Crossfit videos on pushups:
Clapping pushups are a fun, explosive, power-developing variation of pushups. Here’s a Youtube vid demonstrating clapping pushups.
One Arm Pushups
One arm pushups are famous from Rocky training sequences and also a key exercise in one of my favorite body weight training books, Pavel Tsatsouline’s The Naked Warrior. Make sure you spread your feet way apart for balance, and keep your shoulder in the socket so you don’t hurt yourself.