I recently ran into a local musician I know whilst in a severely inebriated state (me, not him, or if he was he hid it well) and got talking about music, as you do. The main point of the "conversation" (really just me ranting while he laughed at me) was that music should inspire emotion (in this case, the argument was that music should make people want to either fuck or fight). It's a statement I stand mostly behind, with some caveats, not least of all that 75% of everything I say when intoxicated should be stricken from the record immediately, and the remainder requires substantial editing to a)remove the sweeping generalisations I'm known for, and b)make it appropriate for the general public.
But that aside, the sentiment stands. Music, or at least good music, should stir some sentiment and therefore make a deeper connection with the listener. Sex and aggression tend to be the two that make the biggest impression (just look at how Tom Jones can still inspire women, and the occasional man I'm sure, to throw their underwear at him, or talk to metal fans about what they like about their music), but there are many more emotions that music can connect with - hence music's use to try and market products, create moods, or manipulate people.
Music that makes a lasting impression tends to have a level of passion and authenticity in it. Most people can detect these qualities in the music they listen to, except, it seems, for many teenage girls and/or Justin Bieber fans. It's not connected to the talent of the musicians, or their songwriting abilities, but almost solely on how they view music and how they approach the creation and performance of music.
There may be studies out there on this, although I doubt it, but I would guess that musicians who make music because they love it and feel driven to do it, tend to lean more towards that authenticity and passion, whereas musicians who see music as an opportunity, no matter how deluded, to make it rich/get famous/sleep with models would tend to lack that level of emotion in their music.
The former make music that lasts for decades, the latter tend to fade into obscurity. Try looking through the Top 20/40/100 charts from 10 years ago and see how many of those artists are still making music, or how many of the songs still sound okay now. My money is on not many, if any...
But listen to music that's been around a while, that has stood that test of time, and in most cases you'll hear the emotion in the music, you'll feel it change your mood - how many of us put on music to cheer ourselves up, to get hyped for a night out, to create a certain mood or atmosphere? That's us making that emotional connection with the music, and that's the music doing what it's been doing since we first started banging rocks together with rhythm.