Do you desire to make people sad when they hear your music? Often sad music is very beautiful, so this is a very good choice. Listen to The Call by Regina Spektor, and you'll see an example of this type of music. Certainly, the lyrics add to the emotional feeling of this music, but even just the instruments, the chords, and how the song is sung gives off a sad feeling.
Maybe you feel like writing a piece of music that inspires people and leaves them with a feeling of grandeur. If such is the case, keep your song's mood in the triumphant/epic genre. He's a Pirate by Hans Zimmer, showcases this mood perfectly.
Ever wanted to make a song which leaves your listeners with a sense of mystery and wonder. Give this mood a shot. With the added touch of solemnity, this Gregorian Chant song perfectly fits this genre.
Perhaps you always wanted to scare people with your music. If so, try this mood. Nazgul Theme from Lord of the Rings is a great example of this. Probably not a good idea to listen to this before going to bed though, unless you don't value your sleep.
Maybe you want to create a piece of beauty and relaxation. Try this mood. A River Flows In You by Yiruma captures this atmosphere perfectly.
Have you ever wanted to transport your listeners to another world, another place. It's time to make use of this mood. This musical piece from World of Warcraft about night elves fits this mood with precision.
If you want to make happy music that's not annoying it might be sort of a challenge, but if you're a classical composer, you have a good chance at making this happen. Listen to The Prince of Denmark's March by Jeremiah Clarke and you'll understand this mood.
I know that's not nearly all the moods, but this covers some of the basics. Also, I know that moods can be combined to create some interesting complex combinations. Experiment with it to see what you can come up with. I'll be back with a post about themes & motifs sometime soon. Good luck composing!