John Carmack revealed in an interview with gameinformer.com, that id Software plans to do sequels for Doom and Quake 3: Arena (1999).

There will be a Doom 4, we don’t have it scheduled or a team assigned to it, but there will be a Doom 4. There’s going to be a Quake Arena sequel.

The big changes at id is that we are going to be starting to staff up for a second team internally. This was mostly driven by publishers who would come to us and say, "We want to do a Quake Arena sequel, or Doom 4. We’ll be happy to work with other teams like the normal id relationship." -- John Carmack