"Watashi" can be used by both men and women. "Boku" and "ore" only by men. "Watashi" is most formal, then comes "boku" and then "ore" (very informal). "Watashi" can be used anytime, "boku" when you talk to someone you already know, "ore" to close friends only.

Don't use ORE with DESU/MASU. Use it only if your peers use it. A good situation to use it: drinking beer and playing video games at a friend's place. That's a very ORE-friendly environment. BOKU is casual. You may want to use it in your daily life, whether you're in DESU/MASU mode or not. You can always use WATASI. You should use it if you're talking to someone you shoud show respect to, like your teacher. All the above assumes you're an adult male speaking standard Japanese. There are regional and age group related variations.