The fact is that you probably like some electronic music right now. If you enjoyed the TV series House MD, you heard a theme song based a Massive Attack's, Teardrop. Grey's Anatomy's original theme song was based on Psapp's Cosy and the Rocket.
Just like some people help you to listen to Classical music, I want to help you listen more discerningly to Electronica. (I'm using that term here mean any music that is produced completely or partially by electronic instruments, as opposed to acoustic instruments with amplification.)
Saying, "I listen to Electronica" is a little like saying "I listen to Rock." It's a very broad range of styles from very soothing, ethereal sounds to driving pluses to virtual noise. Electronica is broken up into hundreds of genres. Yes, hundreds, of which one is "Electronic", so it gets confusing.
In Da Club
Let's start with what a lot of people think of as kid's music: a driving beat, much like the disco beat from the 1970s. The bass drum is playing on 1, 2, 3, and 4; the snare on 2 and 4; the high hat on eighth notes. Genres like this include House, Trance, and EDM. This is the kind of music you often hear in clubs. When you listen to it, first recognise that it was probably written to dance to. It is purposely repetitive but listen for subtle changes every eight bars or so. A very accessible example is Underwolrd's Always Loved a Film. Tiësto's Heroes is a more typical example.
That's Just Weird
On the other end of the spectrum is Intelligent Dance Music or IDM. (This is misnomer. No one would dance to it, and it's not so much "intelligent" as esoteric.) This is the stuff I like. It can range from slightly odd to highly experimental. The common thread is that it usually still has a 4/4 beat in it, often with a very complex drum line. This is the Jazz of electronic music. Some people love, others hate it. Listen for and enjoy the intricacies of the song. Even if the music sounds random, there is often repeating themes and overall structure.
An easy listen is Aphex Twin's Flim. For a more challenging listen, try Squarepusher's Go! Spastic.
If you want to hear something down tempo that won't put you to sleep, "chill out" is your genre. It is characterized by a quiet but driving beat with ethereal layers on top. You wouldn't use this music for meditation, but certainly for work or study. It usually doesn't have to be listened to closely to enjoy. Try Zero 7's I Have Seen to see if you like it.
On the other hand, sometime you want to rock! "Big beat" is the style that was made popular by the film The Matrix. (I'm not usually a fan of soundtracks, but the album from this film is excellent.) The Propellerheads' Take California is an amusing example of a song having a lot of fun with sound bites. This is the genre that is most likely to express overt emotion. Like Funk, the drum beat often plays something on every sixteenth note in the bar, making the sound very "full".
We've seen a good sampling of some of the broader types of music in Electronica, but if you really want see what's out there, try the website Every Noise at Once. It's a scatter map of all the musical genres that The Echo Nest knows about, not just Electronica. It's a great place to discover new music and styles. Have fun!