Looking for RP reasons a race other than Nord would be in Skyrim and be willing to purge the land of its evil denizens. It's easy enough to justify if you're RPing a treasure hunter, but what if you're not? Why would a Breton care about some Draugr-infested dungeon in Skyrim? Why would an imperial be doing anything other than hunting down Stormcloaks?

Um, that's like saying "Why are there X people in Y locations" In real life.

There are literally billions of reasons why people are in a place they're not 'born into'

I'm playing an argonian mutant who prefers colder climates to warm ones... so I headed to Skyrim.

I am playing a Dunmer adventurer, so i guess mine works out.

khajiits decided that the war was a good business opportunity

Argonian from the future. Nuff said.

OP, read this post.

My Mephala worshipping argonian was sent to make the Dark Brotherhood great again, and of course to prevent alduin from eating the world. my argonian himself also wanted power and knowledge (mages college)

My Bosmer thief wanted to evade the thalmor so went to the province most far away from them (also kills them on sight)

My Khajiit fist fighter just wanders the world and ended up in skyrim

Orcs: Strongholds
Imperials: Parents were soldiers stationed in Skyrim, and he/she was born there
Bretons: Forsworn
Khajiit: Caravans
Argonians: Relatives of fisher in Riften
Dunmer: Refugee
Altmer: Thalmor
Bosmer: Traveler/Hunter seeking fortune
Redguard: Coming to Skyrim to help it earn independence from the Thalmor

It's easy, if you give it some deep thought about any possibilities. Not to mention Hadvar presents some reasonable possibilities right at the start.

I'd venture that it all depends on your character's origin; why were you caught in that ambush? Trying to find a lost relative who disappeared in Skyrim? Heard of a business opportunity in a Skyrim city? Once you've established a motivation for your theoretical Breton being in Skyrim, the experience of being there and of being Dragonborn should provide enough motivation to care about the Draugr tombs.

your lovely Nord mother

Because not everyone wants to be a Nord.

If you're roleplaying, maybe you shouldn't care about Draugr-infested dungeons in Skyrim when playing a Breton? I believe a vital part of RP is actually varying your style of playing, including ignoring some parts of the world and the game and focusing on others.

However, if you want a RP-believable reason to do the same stuff, it's not really that different from playing a Nord. Other races live in Skyrim, too - for a lot of people, it's the only homeland they know, whether they're Nord or not. A lot of people from the Empire just happen to live there. A bunch of Dunmer fled from Morrowind into other parts of Tamriel, and a lot of them ended up in Skyrim.

Myself, I like to use the "grudge"-story as a background for RP characters who have pretty much no business being in the area where the game takes place. I just imagine there's someone my character wishes to exact vengeance upon, or someone has stolen something from them. Or alternatively they're looking for a long-lost friend or relative, and the clues lead them to all sorts of places.

You didn't read my post. Why would a non-Nord want to clear Skyrim's dungeons of evil, not just BE in Skyrim.

My Dunmer does not necesarily want to CLEAR dungeons but rather seeks knowledge. Knowledge and curiosity are pretty much driving factors for this game as a Player so it's not really hard to get into.

Well redguards would do it just for adventure. It's adventurious spirit that makes them go to far away places.
Imperials might do it to prove himself to the Nords.
Bretons I guess would be the same as the imperial.
Dark elves would do it to change public opinion on them with all the racisim around.
Thats all I can think of now.

If you're a mage, it's actually easy. Since the Mage's Guild no longer exists, you don't have a lot of options if you want mage training, so you might be inclined to attend the College of Winterhold.

Depends on the dungeon. Is there a particular one you've got in mind? Most of them are tied to specific quests, unless you're just out exploring. Wouldn't you say the quests themselves provide the motivation?

Perhaps you need to think a little more creatively.

For example: Why would a Khajiit, Imperial or even Redguard want to enter a Nordic ruin? Well, that's all up to you. Maybe the Khajiit is a treasure hunter, who doesn't actually care much for purging undead, but for looting? Or the Redguard is a curious adventurer? Or the Imperial see's the undead and his instincts tell him "These undead should die!"?

That's as simple as I can put it. The reasons for the other races doing so much in skyrim could be anything. Nothing is restricting them from doing things in a foreign land.

You could be:

-A refugee fleeing the war in Hammerfell, the Argonian occupation of Morrowind, or the court intrigue in High Rock (all three of these things are ideas taken directly from Hadvar's Dialogue at the start of the game).

-A person seeking to gain knowledge and power through the College of Winterhold.

-A criminal fleeing justice in another province.

-A smuggler looking for business opportunities provided by the war.

-A loyalist or revolutionary looking to support their cause.

-A merchant looking to turn a profit in a new place.

-A mercenary in search of lucrative business opportunities, caused by the war or otherwise.

-Someone who really likes snow.

Funny how this problem never came up in Oblivion. I never once questioned why my Breeton or Redguard would be in Cyrodil.
When I first played Skyrim as my Breton character, it felt weird; like there was something wrong, but I got used to it.

Ehh, skooma run maybe?

Finding a reason for someone to be in the capital of the Empire and mecca of Imperial culture isn't very difficult.

we dont know, why would your character do that? if you want to think up a reason i assume you have, considerd at least, his personality, so just add a reason that fits

Mine was on holiday, but he forgot his passport.

Excellent point. As you've pointed out, the game actually provides you with a template background and a reason for being there in Skyrim. Maybe it's not such a bad idea to listen to the NPC's every now and then, huh?