Pitchers are weird. Ask anybody who's trained pitchers. They'll provide you a detailed list of pitchers' strange mannerisms and quirky superstitions. (Ever seen Jordan Walden's pitching motion?)
No one should be normal though. Pitching a baseball requires consistently performing at a high level of velocity. This places a greater amount of stress and physical demand on a pitcher's body than position players experience. So pitchers need their training to be just as different from their teammates' as they are.
Learn how to embrace your weirdness as a pitcher. Follow these do's and don'ts in your off-season training.
Do run sprints. Don't run long distance.
Pitching a baseball places an explosive, intense demand on your central nervous system. Thus, you need to train in a similar manner. The perfect type of training stimulus for this is sprints—not long distance endurance running, which over time teaches your body to become slow. (See Why Pitchers Must Train Anaerobically for Peak Performance.)
Do active dynamic stretches. Don't do static stretches.
You want your muscles to have a stretch reflex, like a rubber band supplying stored energy when stimulated. Static stretching reduces the ability to be powerful by diminishing your stretch reflex response. (Try this one from Justin Upton's Dynamic Warm-Up.)
Do Deadlifts correctly. Don't use the Leg Press machine.
In my opinion, Leg Press machines are terrible—especially when the Deadlift is so awesome. The Deadlift, when done correctly, works your entire body. This alone should be enough reason to do them. (Learn correct form in Master the Deadlift, Part 1: The Conventional Deadlift.)
Specifically, the Deadlift engages your hamstrings, glutes, erectors, rhomboids and posterior shoulder muscles—all top priority for pitchers.
In order to continually throw a baseball at high speed, pitchers need a tremendously strong lower body. This helps them develop the necessary torque in their hips needed for the pitching motion. Once their lower body develops this power, a stable core helps transfer it up and into their arm for the throw. Strong and stable posterior muscles protect a pitcher from injury.
(Take a closer look at the power of the hips: The Stunningly Simple Way to Unlock Baseball Power.)
Do Push-Ups. Don't do Barbell Bench Presses.
Push-Ups are a great closed-chain exercise. To complete the entire movement, your entire body must remain stable. Barbell Bench Presses lock the shoulders in a susceptible position. This is a good enough reason to leave them out of your training program. Push-Ups are a much safer option for working these joints and muscles.(Train with 10 Powerful Push-Up Variations.)
Do Horizontal Rowing Exercises. Don't do Overhead Presses.
For a pitcher, a weak and unstable scapula is like launching a cannon out of a canoe. It won't work. Upper-body stability problems are tyrants among pitchers, but this is exactly what you risk when you perform a technically sound Overhead Press. Instead, you should perform rowing exercises. They helps to strengthen the decelerator muscles you use when throwing. (Watch the TRX Inverted Row With Jimmy Rollins.)