Do I pay just once for the registration, or are there any fees for keeping the trademark?

During the validity of a registered trademark, there is no need to pay any annual or maintenance fees. The only jurisdiction where this statement would be false is the United States.

There are two ways of filing in the United States, called 'bases' - the Use in Commerce basis, where the trademark is already used in commerce, and the Intent to Use basis, where it's not yet. You can find more information on them in this article, but for the purposes of this answer, let's look at the fees.

For trademarks used in commerce, the owners are required to submit proof of commercial use of their trademark in Year 5, called Declaration of Use. This can be completed by filing a Section 8 declaration. On the other hand, if you are applying for a trademark with a future intent to use it, there's a similar procedure, where you have to submit a Statement of Use within Year 1 to prove the trademark has entered into commercial use. Submission of Declaration of Use and Statement of Use are subject to an additional fee.

Besides that, there are no other annual fees during the 10-year validity period.

After the validity period expires, you may renew your trademark for an additional fee.

One more fee you can encounter during the period would be for a trademark monitoring service, should you decide to subscribe to one. A trademark monitoring service notifies you about other applications similar to your trademark, so you can effectively oppose them in time. Trademark monitoring service is offered by private companies, not the IP offices themselves. They usually work on an annual fee basis.