You've listened to music for years. You have favorite songs that you listen to over and over. You've probably memorized every tiny aspect of a favorite song to a point where you can not only sing the lyrics with the exact same eccentricities as the singer, but you can recreate the unique sounds of the instrumentation. You know who you are.
But are you really listening to your music intelligently? Listening intelligently can make you a much better musician and can help you appreciate a wider variety of music overall.
In order to listen to your music intelligently and appreciate every aspect of it, you first need to actually listen to it. You should set aside time to listen to the music without any other distractions. Sometimes driving in the car can fill this role, as long as you aren't one to get road rage. However you do it, find time to just sit down and listen in a nice environment without working or doing anything else. Now you're ready.
So take a song that you love and ask yourself, what is it about this song that I love so much? Is it the melody? The overall groove? The lyrics? The singer? Remember that the lyrics and the sound of the singer are two very different things. Maybe it's something more subtle that you like about it, like the constant juxtaposition of two melodies, or that it just seems to almost overwhelm your ears with sound and music (known as a wall of sound; one of my favorite techniques). Understanding precisely what it is about a song that you like so much will help you find other songs that you'll enjoy.
Keep listening. What else is good about this song? What else did the artists simply get right? If it really is a good song, it probably has a nice flow from beginning to end, meaning it never gets boring and no individual part outstays its welcome. It also probably has interesting and pleasing chord progressions. Interesting chord progressions are key to a great, memorable song. Artists who enjoy enduring popularity over many years all tend to have that in common; they all know how to make interesting melodies and chord progressions. You can say all you want about the importance of lyrics, and you would mostly be right, but I can guarantee that the Beatles' Yesterday would never have been remembered if McCartney wrote it in the style of, say, Jane's Addiction's (lack of) melodies and chords.
Also, think about what genre or sub-genre the song most closely resembles. Are they incorporating multiple genres? Are they adding some style in this particular song that they don't usually do? Maybe a different time signature than the usual 4/4?
Now get a little more technical with your listening. Try to locate and differentiate each individual instrument. Where in the stereo mix is the singer, guitar, bass, percussion, keyboards, synthesizers, strings, voice samples, saxophones, sousaphones, whatever? How loud is each part in comparison to the others? Do you notice an excessive amount of bass? Or maybe not enough? Sometimes you'll hear a song that, while clearly well written, will sound kind of blah or flat to you. This isn't just some ethereal impression you're getting; it may be because of the way the song was recorded or mixed. If the recording doesn't fill the whole spectrum of human hearing, it is at great risk of sounding underwhelming to the listener, regardless of how good the music itself is.
Clear, crisp high end (hi hats, egg shakers), rich middle-range (vocals, guitars, cymbals), and deep, satisfying bass (kick drums, timpani, low horns), all need to come together to make a truly fantastic listening experience. To really understand how this works, get and listen to both Queen's first album (self-titled), and their fourth album, A Night at the Opera. Go do it now. I'm serious. I'll wait.
Both albums display incredibly good compositions and musicianship. But their first album is low-budget: it's scratchy, distorted and is completely lacking in satisfying bass. The treble sounds muffled and frankly, kind of weird. On the other hand, A Night at the Opera was the most expensive album ever produced for its time, and it shows. Notice how, in the newer album, Queen's music opens up in a completely new way. Hear how the whole frequency spectrum is filled? You can really hear the kick drum properly, the acoustic guitars are crystal clear, and their trademark opera choir (which is really just the four of them overdubbed like 10 times) is loud, powerful, and never once overloads. Yell into your crappy computer microphone if you want to hear exactly what 'overloading' sounds like.
A well-produced album will have presence. It will transcend the speakers that they're playing on and become part of you, the listener.
For the other end of the technical spectrum, try listening to a very old (around or before the 1940's) or very amateur album. As you listen to it in addition to really nice albums, you'll start to understand what makes a beautiful, full sounding recording. You will start to hear that presence I just mentioned, on a conscious, rather than subconscious level.
Listening to music with this kind of trained ear takes some of the mysticism out of music, and some may not like picking apart everything they hear. But for me, a composer and producer, the rewards for hearing everything with a heightened awareness are immeasurable. Understanding how different elements interact with each other and what makes good things stand out is extremely important when making your own music.