Roads are important indeed. Those are my favorite improvements.
Farms and nets/fisheries are usefull if you want to make your cities grow faster. If you build a city in a polar region nets are essential - otherwise the city will starve.
I almost never build mines, because of polution problems. Sometimes I build them early in the game on planes/grassland to speed up production. I can always change those tiles to farms when polution becomes a problem.
Latter in the game, when you'll have enough PW, you can terraform desert, polar tiles, swamps and dead(polluted) tiles, because those tiles don't give you much resources. It's also cheaper to build road-like-improvements on grassland/planes.
As you can see tile improvements are important, but it's always more important to prevent your cities from hostilities.
