Generally not as CFL lamps are designed to put into a specific type of fitting and the fitting will have a maximum set wattage that it can handle.  You may also find that different wattage bulbs are different sizes as well being that you will struggle to fit them into your fitting.

Why can I not exceed the maximum wattage rating?

The maximum wattage rating is a critical safety limit set by the manufacturer. Exceeding this limit can lead to overheating or electrical overload which can trip the circuit or potentially pose a fire risk. 

How do CFL watts compare to Incandescent watts for light output?

CFLs are far more energy-efficient than traditional incandescent bulbs.  Often using less than half of the same amount of wattage as the equivalent incandescent bulb.  When you are choosing a replacement of a newer technology of bulb it will help to focus on the lumens (brightness) rather than the watts to figure out which bulb you need to purchase.  If the equivalent wattage is not listed for the replacement you are looking at you can compare the lumens and if these match or are similar this will confirm it is the correct bulb to buy.

Specific Considerations

What should I look for on my light fixture?

The maximum wattage will normally be printed or stamped on the fixture's socket, housing, or on a small label near the socket.  It will say something along the lines of “MAX 60W” or “Use only with a maximum 13W CFL.” 

Are there any issues with dimmers?

The bulb should advise on the packaging if it is dimmable, if it is not you should make the assumption that it will not be dimmable.  Using a non-dimmable CFL with a dimmer can damage the bulb's electronic ballast, causing it to flicker and make the warranty invalid. 

In Summary

You should use a different wattage of CFL lamp in your fitting as the fitting will likely be made to support a particular wattage.  When replacing your CFL lamp you should make sure that the wattage is the same and that it is dimmable if you need it to be dimmed.