In general, you can use different colour variations of your logo; however, the protection depends on the version filed with the IP office. The choice to file in black-and-white or in colour depends on the jurisdiction, with a few examples being:
It is a common practice to file in black-and-white in the US. That way, all colour variations of your logo are protected. If a third party uses your logo in any colour, you'll have the legal grounds to stop them.
In the EU, marks are not commonly filed in black-and-white if used in colour. If you file your figurative mark in black-and-white and your competitor uses the same mark in colour, the marks would not be considered identical, and enforcement of your rights would be very difficult. Therefore, if your logo trademark is used in colour, it should be filed as such.
You can consider registering the version that you are using the most frequently with your goods and services. Be sure to submit the version you actually use - if you use your mark in a different colour version, you'll have a harder time proving infringement.