Suggestions for a clical music beginner?

I listen to all kinds of music, but not usually clical--I prefer rock, rap, country, and I like to listen to jazz live. I do find clical music relaxing though, and I'll be flying across the Atlantic this weekend so I'm looking for any recommendations I could download for the trip. If anybody has any recommendations, sort of "clical music for dummies," the more famous works that an educated adult should be familiar with, I'd really appreciate it. I'd like to have a few "greatest hits" type CDs for a couple of the more famous composers--Bach, Mozart, Beethoven, etc. If anybody can suggest a few compilation CDs of famous works I'd appreciate it! Thanks!