You can get dimmable CFL's, you just need to look for them (and they cost more). Usually, there is a large "Dimmable" label on the package. If not, you have to read the small print around the base of the electronics portion of the lamp. Most will say "not for use in dimmers".
Even if you get dimmable ones, they don't dim as nicely as incandescents. You can probably go from 100% to 50% brightness, then they abruptly cutoff. They also don't dim as easily when they are cold. So if you've dimmed them down as far as they go and have a dimmer with a separate on/off control which "remembers" the dimmed level, they may not come on when you turn them back on if they are cold. You'll need to go to full brightness, wait a minute for them to warm, and them dim them back down again.
LED based lamps also come in dimmable and not, but the LED ones don't have as many issues. Costco has some dimmable LED A19 40W equivalent bulbs for $10 each which I like better than CFLs, except the color temperature of the LED was not as nice as the CFLs. But at least they have more dimming range and come on to full brightness right away.