Not all dimmer switches are the same, and if you buy one that's not rated for the total wattage of the lights it controls, you could have problems. Check the fine print before you buy.
Make sure the wattage rating on your new dimmer is at least as high as the old one.
If you're dimming CFL bulbs or LED bulbs, make sure you buy a switch that can handle the wattage and that can be used with those types of bulbs.
If you’re installing a dimmer switch, keep in mind that each switch is rated to handle a maximum wattage. If you’re trying to dim six 100-watt lightbulbs, use a switch rated for at least 600 watts. Newer models are fairly generous with their allowances (usually about 600 watts), but that won’t cut it if you’re trying to dim seven 100-watt bulbs.