I don't have a miniatures collection. This is probably one of my biggest hang-ups when it comes to running a game.
I like minis. I enjoy the tactical and tactile aspect of setting up the battle-mat. I like the sight of them on the table, and I like the focus they give to the game. You break out the miniatures and everyone pays attention.
Problem is, I just don't have the money or time to build a collection. (And, unlike Gary, I don't have kids with their own toys I can steal and kitbash. Besides, kids are going more with video games these days.)
I get around this with a bunch of kludges, but I don't really like any of them.
Often I just don't use the tactical map at all. Especially for older versions of D&D, it's often unnecessary. You can discuss tactical positioning and make rulings on the fly all without positioning little figures. It can get difficult with areas of effect, however, and it can be difficult to keep moment-to-moment cohesion of vision and communication, especially in larger skirmishes.
I have in the past experimented with using paper minis, mostly for the PCs. This can work well for the pure representation aspect, but it always feels cheap. There's just something tactile and pleasing about small three-dimensional figures, and especially so with the added weight of pewter. It's the difference between playing chess with a cherry-and-marble set vs. the Milton & Bradley plastic version. It just doesn't feel the same, and it doesn't draw me in.
Another thing I do is to use dice to represent the monsters. This actually works well, and I like it. Dice come in enough different shapes and colors that you hardly ever have trouble remembering what's what, and instead of having to mark the bases they are themselves the markers. Rather than 'that hobgoblin mini in front' you're tracking 'red six' or 'white eight', which is nice. Plus, it gives large groups of monsters a more cohesive effect than if they're all represented with minis, even similar ones. A tribe of orcs is a bunch of six-sided dice, and visually - even with different pips showing and different colors - there's a sameness about them that marks them as 'together' and 'different from the PCs' in a way I like. At the same time, if you want to mark off some monster or group thereof as 'same but different', e.g. these hobbos are carrying polearms instead of swords, that's really easy - use different colors or numbers, but the same shapes. Also, there's the effect of pulling out the d100 or d30 for something truly Big and Nasty, which I like better than pulling out some custom mini for the Balrog or whatever-it-is. Using a die adds to the mystery: the monster is more of a cipher in the players' minds, rather than a concrete representation, and that adds to the fear and tension.
There is one big problem with this, though: it doesn't work well with paper minis. With paper minis it just takes the 'cheap' feeling and emphasizes it. If you have a few boxes of painted pewter to represent PCs and important NPCs it's different, because you have those nice figures there on the table in contrast, but without it just attenuates the link even further.
I'm not going anywhere concrete with this. There is no solution, per se, except for me to buy and paint some, or pony up even more to get them pre-painted, which isn't going to happen. At least not anytime soon.
Broadly speaking, gaming without miniatures is certainly possible, and even in some cases (or partially) preferable. But having a collection of painted and ready-to-deploy is definitely a luxury that I'm missing, and I think it's part of why I'm a little reluctant to put myself out there as a person actually willing to run an actual game.
I should get over that and run anyway.