Circumstantial, but many games can benefit from it.
Personally I think it is the multiplayer games that benefit most. Just look at Unreal. From skins to new guns to new game modes and all sorts of nonsense. Mod communities are probably what keeps these old shooters going.
And Half Life. Pretty sure Counter Strike, Team Fortress, Natural Selection and god knows what else(Red Orchestra?) all started off as mods. And they too get modded.
Custom maps for Warcraft/Starcraft? Spawned entirely new genres. The goddamn MOBA which is so damn popular. All those tower defenses that won't stop multiplying all over my phone.
And they are nice to have for stuff like Skyrim, granted a lot of it does miss the point and throw game balance out of the window. But hey, nobody's ramming all the mods in your face. Some people enjoy completely messing the game up, some not so much. Some like to do it as an afterthought after clearing the game properly. And there are plenty of mods that do attempt to take game balance and progression into consideration. Though really, Skyrim's own balance is kinda way iffy anywaaay that you can break it without mods.
The way certain games are sold these days does mess up modding. Where do mods come in when everything is tied to an account with level progression, leaderboards and all that jazz which is considered standard issue? With the dev/publishers having full control over the servers? There's a certain clash.
And there's the whole consoles not working with mods, which is rubbish. Just look at Trials Evolution. I mean seriously, you can make entirely different games in it. Halo itself at the very least has Forge and flexible game rule options. And with players deciding their own rules can lead to all sorts of nonsense. I never thought Infection would be anything but what it was, but hey we turned it into Rocket Launcher Hide 'n Seek.