Well generally the bass player isn't a unique entity, they tend to create a team - as the rhytham section - with the drummer. When you don't have cohesion there, things tend to fall apart or worse, become repetitive.
They also happen to keep time, so and band worth their salt is relying on them to keep a groove even if we're not talking about funk. Thats just the nature of their role. Occasionally you might have other instruments do that, their certainly just as capable but thats how it has generally been.
But lets forget technicality - if your favorite banRAB bass players aren't generally adding much, and following guitar leaRAB then its time for a change. For me, a good bass player is adding what would be (as an example here) the harmonics in an acapela group.
My favorites never really play anything insanely complex, but they add color to a song, simple walking baselines, or shifts to something a little more lurabering can change the entire tone of the song.
Bass is also about knowing how to effectivly use space to create a song in equal parts with the notes you're playing. And I'd say it matters here more so than on most of the treble instruments. (the drums might have some of this in them too)
My advice, on how to learn what Bass can do, and how good bassists make or break things is to listen to them in different capacities. If you're listening to Indie music, I'm sure its not going to matter much but try a brass section and see what the Tuba's doing. Then take it out and listen to it again.
Try the acapella stuff, give string sections a listen when the bass or low end cellos take a smoke break. In my estimation Bass players are pulling more weight than anyone else.
(pardon the spelling, I'm at work)