Clean guitar player's second best friend, tremolo
The main reason many guitar players don't know about the tremolo effect is because of overdrive and distortion. Tremolo usually doesn't work there. I'll get back to that in a moment. But when playing clean, it's your second best friend.
Two things to note before continuing.
Second, the best friend to a clean guitar player is, of course, compression. If you play clean, you need that. And as far as which chain order you should have, you can go either way with compression first, tremolo second, or tremolo first, compression second. It depends if you want the "strike" to be heard first from the guitar sound or the tremolo effect. You'll have to experiment to see which chain order works best for you. But it's absolutely true that the less noisy way is compression first, tremolo second so you're not compressing the tremolo effect itself.
Tremolo is a really easy effect to miss, because as said above, most guitar players drown their guitars in way too much overdrive or distortion.
However, if you dial the overdrive back to a civilized level, you can ring out some really cool sounding stuff with an overdriven tremolo sound.
Typically, tremolo works best on the bridge side (as in the rear) pickup whether clean or overdriven because it allows the effect to be heard more clearly. This doesn't mean you can't use the neck side (as in the front) pickup with the effect, but to make that sound right, a generous amount of compression helps quite a bit.
Tremolo works better with chords than solos, but if you must solo, the nice part is that you can do long droning notes and the tremolo effect carries things along quite nicely. There's no need to go all over the fretboard when the effect is in use.
Is tremolo a one trick pony?
No. And the reason for that is simple. You can adjust the depth, wave and rate.
Slower, wider tremolo effect sounds completely different compared to a faster, shorter stutter. You can go anywhere from full-on country tone to '60s acid rock to '80s new wave and several other genres all from this one effect.
Clean is where tremolo sounds best, but as noted above it does work with overdrive, provided you keep it civilized.
Pick yourself up a BOSS TR-2 and you'll love it. Or if you have the effect in your virtual rig or multi-effect amp or pedal (they all have tremolo buried in there somewhere), use it. Tremolo is a great effect to have in your tone arsenal.