Fiery Dragon and several other companies make flat tokens that can be used, and have illustrations on them. Fiery Dragon also sells them electronically, and you can then print them on uncut label sheet, and stick them to better materials (like wooden disks or poker chips) for more durable tokens.
Several RPGs of old made extensive use of them; The Fantasy Trip, GURPS 1E (via the Man to Man boardgame using GURPS 1E rules), DragonQuest... D&D 3 & 4 both suggest such tokens and illustrate using them instead of minis.
Stealing counters from old board games is an 'ancient and honorable practice'... it's actually implied strongly in the whitebox D&D rules to do so with Avalon Hill's Outdoor Survival... which has a number of animals and people.
Any material bit that's small enough to fit your battle grid can be used in a pinch. Dice, boardgame bits, coins, scraps of paper, buttons.
Paper miniatures, either print your own from the image files or PDFs, or preprinted ala SJG and PI Games' offerings, are a very viable compromise. Light, inexpensive, nice to look at, and (for print-at-home) readily replaced if lost. When I make them, I print on 110# card, have the player color them, then I laminate them with Con-Tac clear non-glare laminate or with clear tape (front and back, BTW), then cut and fold them, and use rubber cement to attach a penny or washer as a base weight.
If you have the motivation, heavier card (like posterboard for school) can readily be used; print on good bright white paper, and glue it on. Then laminate and cut.
Various toys also are not uncommon. I have used Lego minifigs, Playmobile knights, Action Figures, Micromachine figures, toy soldiers, and other such options.
If you have a good cold-ink inkjet, you can also make VERY nice stand-ups using the blank Shrinky-dink sheets. Print on them, color them, then shrink them in the oven. Or tape it over a picture, trace the lines in black, color it in, cut it out, and shrink it. You can even order the stands to make them stand up from the manufacturer.