I think most of us have different ideas of what makes side-missions boring and games "too" repetitive.
What I think of as 'too repetitive' others might not and vice versa.

Examples of games where I've enjoyed the repetitiveness:
Isenwald, Xenonauts, Dead State, Mad Max, Red Faction Guerrilla, Just Cause 2, Mass Effect...just to name a few.

Basically:
* isometric and tactical stuff
* any kind of racing
* extreme violence and destruction
* what I consider to be interesting and immersive game-worlds (Mass Effect)

My suggestion is that if you enjoy the game mechanics or the result of it, or the settings of the game, it is less likely to feel repetitive for you. It sounds intuitive enough but is a point I feel is often missed in the discussion on games.
Especially since media and critics tend to look at games from the same perspective regarding what is a repetitive game or not, so the notion of them representing consumer interest is highly limited in scope.

Assasin's Creed 1.

Nuff said.

Very very good point, are not most games repetitive in some way after all. I have lived for many years and have had my fill of some games' repetitive game mechanisms in spite of not minding them twenty - thirty years ago.

For one, I think keeping the environments diverse helps with elevating the sense of repetitiveness and boredom. Side-quests in many RPGs might be repetative if you take a proper look at them, but as long as one has me exploring some ancient dungeon, another a magical foerst and yet another a floating castle or something, I'm likely not to notice it so much, and the same goes for other genres. One of the reasons I hated Swapper was that it was always nothing but the same dark, blue-grey murkey featureless corridors and rooms. I just got so tired of the tedium of "walk into a blue-grey poorly lit room, solve a puzzle, repeat" that playing the game became almost physically painfull.

Of course there are exceptions. Legend of Grimrock (the first one) has little variation, and yet the game never felt boring to me. In fact, the opressive atmosphere of the dungeon is an important part of the game. The more diverse world of LoG 2 was however a good change.

All games are repetitive, principally as they follow rules. Imagine a game where your controls changed randomly throughout the course of the game.

It's boring the instant that it feels like a repetitive chore :P

For me, all relies in enough differences over time that keep the illusion.

For example, the core of action RPGs like Diablo1\2 is super repetitive (click&kill), but various landscapes, quests, monsters, items, skills make them very addictive and interesting (in my opinion).

Same for platformers (run&jump) or RTS (build&conquer), if you have enough things to do.
Probably simple infinite puzzlers and sport games are those that I stand less.

Obviously you can burn out on a genre, if you play too many samey titles in a row.

EDIT: some people, however, just like the competition in games, so they don't care about repetitiveness.

Thinking about it, I guess there are three important aspects to whether something is perceived as repetitive or not.

The most obvious one would be fun: Is the action you're repeating enjoyable to you? Does everything work as intended, are the mechanics interesting, the controls intuitive, the effects satisfying? Is it a challenge or frustrating, exciting or bland, relaxing or annoying?

The second one would be freedom: if you are allowed to try different approaches each time you repeat something, it's less boring than if there's only one preset way to do it; and if you repeat random things by choice it's more fun than if you're required to repeat specific things in order to advance the game.

And the last one is reward. Does it actually pay off to repeat things? Is the result worth the time you're investing? Does it make sense, does it feel natural, or does it feel forced and put in there just as uninspired filler content to artificially prolong gamelength? Do you get to see new places, fight new opponents, try new techniques, see your character develop quickly, or do you feel like you're not making any significant progress?

When there is nothing to look forward to in the game.

For instance, I'm mostly fine with repetitive grinding in CRPGs... if there is some great skill or spell I am looking forward to acquire for that grinding, or afford some kickass weapon or armor. Diablo 2 and Baldur's Gate 2 managed to achieve this, I recall trying to find all the needed pieces for some magical item (gem or staff? I don't even recall anymore.) in Diablo 2, or trying to get all the needed pieces for the Flail of Ages or somesuch in BG2 + The Throne of Baal, or finally achieving to kill my first dragon in BG2.

Or it might even be merely the story, wanting to see how it all turns out and ends, which keeps me going.

Then on the other hand, here I am playing The Elder Scrolls: Arena with much boredom. I have so far collected 3 out of 8 pieces for The Staff, which is the main story campaign in the game. The problem is I feel the game has very little to offer to me anymore. My character has all the important skills near the maximum already, I think I know all the spells in the game already, and the dungeons and cities are so similar (even if they have a bit different textures and graphics) that there is no incentive to even visit new places. I could just as well drop the game already, long before I have finished the main story.


Then to something completely different. I regularly play also an online shooter, Team Fortress 2. Apart from rarely receiving some useful new weapon or item I didn't have before, it is mostly the same all the time. I even tend to play the same maps all the time: Well, 2Fort, Sawmill, Double Cross, Turbine, Doomsday.

Sometimes I get bored with it, but sometimes the competitiveness keeps me going. A bit like playing soccer or Texas Hold'Em with friends, the game remains the same but still you find a reason to do it.

Wasteland 2 (grinding).

I don't have any problem whatsoever with repetitive games. I'm thinking more into grinding into games like Diablo 3, Path of Exile, a lot of JRPGs, or generally, open world games. All that matters in those cases are the mechanics. If mechanics are good, the game is enjoyable to play, i like doing same thing over and over again.

I hate more linear games that, even if they might not have repetitive content, as you get different monsters/bosses, etc, they force you playing using a bad mechanic. I'm thinking about games like Half Life 2. I hated the missions where you have to drive that boat around, but i don't have any possibility to skip those missions. While you didn't had repetitive environment, as you had to do different things, the repetition of a bad mechanic can be more annoying.

As RPGs go, take something like Xenogears. You have repetitive gameplay and environment. By just moving around, encountering and fighting random monsters is inevitable. Nevertheless, the combat system is great, so i don't have any problem repeating it.

Some rare gems can afford repetitiveness, like you said, it's: deep RPG games, rare strategy games, rare cyberpunk games for fans of the genre, space and racing games. For example, Skyrim, Deus Ex HR and Witcher 3 have brought nothing innovative, but they're diamonds between stones and coal.

Dungeon Siege

I do think the major fault of AC1 was the storytelling; all the sequels were repetitive as the first one, but the way the story was told was more involving, rendering the repetitivness more bearable.

Games start feeling repetitive when they fail to introduce enough new wrinkles to the gameplay as you progress. The reason Assassin's Creed is boring is because techniques that allow you to succeed at the beginning of the game are for the most part the exact same techniques that allow you to succeed at the end. I played AC for the first time not too long ago and I felt like I was basically just doing the exact same mission over and over again, with little need to actually think about how I was playing.

Costume Quest is another example - very charming game but the way I beat the first enemy was exactly the same way I beat the final boss and every enemy in between.