I have been listening to internet radio with Pandora for several years and I really like it!
Pandora is based on technology developed in the Music Genome project: an effort to give each song a unique digital fingerprint that consists of almost 400 attributes and a special mathematical algorithm to create playlists based on the attributes of a given song. So when you create a Pandora "radio station" you simply give it the same of an artist or song that you like, and it will automatically build a radio station using those songs as a reference point. As you listen to each song, you can give the songs a thumbs up or thumbs down and the AI in the site will use that feedback to tune your radio stations to play more songs that it thinks you will like based on your feedback. The more you use Pandora, the better it becomes at predicting what kinds of music you will like, and it makes your radio stations sound better as a result.
When you listen to music on Pandora you are streaming music from a cloud. There is also a rich amount of information on the songs and artists that you can access while the songs are playing if you want to learn more about the song or artist. They also provides links in the site while the music is playing that allows you direct access to digital stores (iTunes and Amazon) so that you can buy the track or album if you would like.
There are other music streaming options. Slacker, Rdio, Spotify, Last FM, SOMA and many others. I am also a fan of listening to SOMA radio periodically. Have a look for yourself online, I am sure you can find something you will like :) If you want to hear a song again without buying it, try youtube! Most songs can be purchased for $1 or less, so if you really like one and want to be able to take it with you running, in your car, or other mobile situation and do not want to use a smartphone to stream it, or need to conserve your data, having the song file locally can be very nice. I have thousands of songs in my personal music library and I use iTunes to create "genius" mixes when I listen to them.
Give Pandora a try, I think you will like it. They have a huge index of songs to choose from, so you are very likely to find music that fits your listening preferences. One of my favorite stations is based on the artist "Liquid Mind"
Music can be a very relaxing, energize, mood modifying source of enjoyment! Music has been enjoyed throughout human history in all sorts of forms. Making music can also be a lot of fun. Think about learning to play an instrument. Listen thoughtfully.... would you like to be jamming on the keyboard, singing, playing the beats? You can also give digital DJ'ing a try to get more into music: make playlists with your music and see what you can do. Music can be active or passive! Music can be anything you make of it!
My post is about Pandora, so here is a web link to the Pandora Internet Radio site :) Enjoy
I find that listening to music has a stimulating effect on me in general (with a few exceptions of special space out/ ambient types), and that I am unable to sleep if I hear music with lyrics or a strong beat. I used this property of music to help me study for many long hours deep into the evening while lite on sleep when I was studying to become a scientist in college, along with green tea, it worked wonders :)
What I like to listen too has undergone a consistent shift over the years. I tend to appreciate a lot of songs from many different genres of music. I like ambient, electronic, techno, dub-step, alternative rock, electronic rock fusion, jazz, smooth jazz, classical, pop, synth-pop, progressive, trance, house, classic rock... I like anything with good lyrics, solid composition, and a nice beat! I dislike sleazy, strange or weird lyrics. I tend to like songs that convey or are motivated by strong emotions. Even after writing what I just said, I cannot accurately convey my music preferences. Oh well :P