I know that using console commands will disable steam achievements in some games. Will using mods in e.g. Fallout new Vegas disable achievements as well?
It depends heavily on the game.
For instance, Invisible, Inc uses a system to detect modifications to the game code and will disable achievements. There are workarounds for bypassing the mod achievement disable, but it's not trivial to do.
On the other hand, many games do not care if you use mods for achievements. Fallout: New Vegas is in this category. I even made my own mod to get the Caravan achievement.
Other games, like Civilization 5, have specific achievements surrounding the use of mods. You have to use mods in order to get them.