This is one of the greatest collections of art in the world. Too many people rush through the rest of the museum just to see the Sistine Chapel, however. For a good overview of the museum, you'll need to allot at LEAST 2 1/2 hours to see everything. For art buffs or those whose feet are more up to the task, plan on 3-4 hours.
If you are a budget tourist and happen to be in Rome the last Sunday of the month, the Vatican is free. If you plan to see the Vatican on the Sunday that it's free, get to the museum at least 1/2 hour before it opens if you don't want to stand in line for up to 2 hours just waiting to get in. In the off season it's not so bad, but I still recommend shelling out the L18,000 and going when it is less crowded. Since the museum is closed Sundays, Monday's seem to be busier than other days. In off season, you can show up about the time the museum opens and only have about a 10-15 minute wait.
Aside from the Sistine Chapel, Raphello rooms, and the Borgia's Apartment, there are scores of other religious art. There are halls of tapestries, map rooms, Greek and Roman statues, a very interesting gallery of modern religious art, a surprisingly unbusy gallery of ancient Eutruscan artifacts, and a Pinacoteca full of paintings of Christ and the Virgin Mary.
Museum hours are 8:45 - 16:45 from April 1 -October 31, and 8:45-13:45 from November 1 - March 31. The museum is closed Sundays and all federal and religous holidays (if you don't know your Catholic holidays, you'll need to get a guidebook that lists them or call ahead to make sure it's open). From personal experience, March 19th is a religous holiday. I couldn't tell you which one, but we showed up at the Vatican to find it locked tight.