RPGs have their origin in tabletop wargames. There’s no getting around that history, and the fact that, as a result, miniatures have been a feature of RPGs pretty much from day one. The question, of course, is whether to use them or not, and if so, when.
I’ve mostly been running theater of the mind games for the last few years. Partly, this is a function of genres. Science fiction games and mixed settings like Rifts have some really long range weaponry available, such that the scale of minis doesn’t necessarily line up well with the scale of the battlefield. Long range for a Glitter Boy Boom Gun is 1000″. Unless you happen to be playing on an 85 foot game table, that’s not really going to work out well. Supers games with a lot of flying characters are another example – that’s just hard to represent on a 2-D table with minis.
With that said, operating without minis presents some challenges. What exactly IS the range from that Glitter Boy to the APC he’s shooting at? How many bad guys are ganging up on the hero? As a GM, you need some method of resolving these issues. I’ve generally used dice to help out. Using spare dice, you can track things like the closing distance between two forces and the number and status of enemies engaged with various characters. That, plus a little narrative winging it, generally handles most situations just fine.
Minis are fun, and if you have the right ones available, they can add a lot to a game. But if you don’t- well, constantly reminding the player that the lizardman mini is actually the High Martian chieftain and the elf is really a cyborg can really mess up the immersion.