As usual, this doesn’t apply to all games. Make considering if this fits your game a top priority before moving on.
Game modes, they’re very lovable, and usually a great addition to a game that has the gameplay and/or content to support them. A wide variety of different game modes can extend playtime (though that shouldn’t be your goal when implementing them) as well as make for a more fun, varied user experience. This all falls apart though if your execution is terrible. From the perspective of a user with a rather sub-par developer’s eye, let me try and see if I can explain how to do it right.
I mentioned it before, I’ll talk about it here again. First and foremost, your game needs to be diverse enough so you can actually do something interesting with it. This can come from two sources.
If your gameplay has lots of different parameters you can tweak around, try and see if anything makes for some drastic changes to how the game’s played. Does it still feel like your game, and is it actually fun? Think of a way to use that to your advantage and make a game mode out of it.
Content can be a huge contributor here, too. Got boss fights throughout your game’s storyline? If they’re interesting enough, a “boss rush” mode might be cool. Lots of randomly generated content in the form of loot? A gear tester mode might be useful and/or fun for people to mess around in. You know, sort of like a sandbox mode.
You need to tread carefully though. Sure almost every game can be fit with some sort of “trial mode” (race with or against the clock), but that doesn’t necessarily make it a good idea. If you don’t think it through you’ll end up with a game of which the extra content feels really tacked on, like it was put there as an afterthought, “oh yeah we can easily add more stuff if we do this”. That’s obviously not a good thing. Execution is everything. Just adding a timer or changing some numbers doesn’t even come close to good execution.
Maybe your game’s fine without tens of different game modes though, even if it would support some pretty cool ones. Sometimes the absence of this or that game mode even adds to the fun of the rest of your game. If your game rides strongly on visuals and amazing impressions, not having a “boss rush” mode helps the bosses keep that special feeling. “This is so cool, but I’m not going to experience it again anytime soon, so I better cherish this.”
Do as you see fit. As long as it’s fun.