Nope, there is no limit on the colors.
There are design firms out there who charge depending on the number of colors they use in a design - which is silly. It's just a way to get you to pay more for the exact same thing. Using more colors does not cost the design firm anything and it does not take more time.
But colors do have an impact on printing costs. Depending on the printing company you use, a full color design will normally cost more to have printed than a 2 or 3 color design.
It's a good idea to phone up your local printers and talk about prices before we start the design process. That way you know beforehand what your limitations are and we can build your killer logo within those boundaries.