
There are far more ideas than I've had time to implement of course, which is okay because I know I'm gonna be playing this game for years anyways. Some of these characters would never work in Oblivion, especially since I'm playing the vanilla game (I'm on PS3).
Feel free to share your own Skyrim roleplay ideas.

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The Bandit:
This one will be a male, either a Redguard or a cat-person. I've never played a Khajiit, so it's possible my bandit will be a cat-person.

The bandit will travel the road until he finds some sort of an encampment he can take over by the side of a busy road, possibly inhabited by other bandits. He will take this encampment over and live there as long as it seeems fruitful. During his time here, he will simply sit and watch. He will wait for travelers to drift by. Those travellers which seem weak? He attacks them! Guards and such will be avoided if possible, although perhaps an eventual bounty might change this.
He will be very much like a medieval bandit, in other words, who waits by the road in ambush.
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The Cleric:
I've already made a cleric. Clerics often were played as support characters during the great Dungeons & Dragons days (before videogames took over the genre). They are not usually in the midst of battle. their role was often on the sidelines: healing up the fighters, keeping them alive as they fought monsters head-on.
In Skyrim the cleric is still somewhat of a support character, I've noticed, but he or she can wind up fighting enemies head-on as well. Claire Voyance (Breton, currently Level 28) hooked up with Brelyna at the Mage's Guild College. I was originally trying to play Claire Voyance as Restoration, Illusion, and Alteration-only, but she eventually had to take on some Conjuration as well.
Brelyna usually took the role of the magic-user during battle, with lots of Magika to spend. Both Brel and Claire could cast Summon Fire Atronach, so both usually did so. After this, Claire would be free to support Brelyna at times, healing her up, and casting certain helpful spells as well.
But the Cleric isn't as specific as it was in DnD, where we could make large parties of PC's, each character playing a specific role. Eventually, the Cleric must also become part-fighter and magic-user as well.
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This is the third and final RP idea I'm going to present, as it's already 6:10 pm and I need to get dinner started.
The Paper map
When I first got Skyrim, I opened the box, and then purposely made myself not look at the big, tan-colored map. I didnt' want any spoilers. I didn't even look at the 3d in-game world map. I didn't really need to, since me and my first 2 characters mostly spent all our time in the Riverwood/Whiterun area. I spent a LOT of time in this area folks!
But at some point during my 2nd character's existence (Thor a'Zaene the mercenary fighter I mentioned earlier), I figured it's possible Thor could have a paper map. Then the idea was born. Why yes! He has a paper map. He can look at it in any time. It'll be hard as heck to find locations during future quests, but I like a challenge! I need challenges! Can it even be done? Can we use only the paper map and find our way around?
Turns out, it is possible, but very very hard. I eventually decided that as long as Thor is in a town, he's allowd to look at a "better" map than the paper one. If he's in a town, I therefore will look at the 3D map. I'll look at the area where the next quest marker is, and I'll try to mark its location with a pencil on the paper map. You have to use pencil.
Once he's out of town, I'm no longer looking at the 3D map, only the paper one. There's an X on it, jsut as if he's got it marked by somebody in town, and now this map is tucked away in his backpack or something. I keep reminding myself I need to find a place that'll copy the paper map, this way I'm not always putting X's on it!
I personally feel it's far more immersive this way. I have a theory Bethesda actually included the paper map for roleplay purposes, for those of us who are hardcore enough to try it! I've tried it and it's challenging, but for those who persist, it's a good way to really get into the game.
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Pasta's boiling...here's one more idea.
The Scout
The Scout is another idea which stemmed from the map one. The scout (the way I'll eventually play him) will only ride his horse through rough territory. He will not do any dungeon diving. Instead, he will be a support character to other characters I'm gonna make in the future: especially dead-is-dead types.
My Scout will be an American Indian looking character to start, but looks aren't really that important. Neither is race. Here's how The Scout works.
Let's say I've got a character who's supposed to go on a quest in some remote, uncharted location. We'll call him Character #1. The Scout will go there first. He'll ride a horse (gotta have a horse), and get a feel for the terrain and any enemies which are about. As he travels, I'll be using the paper map idea, taking notes as we go.
Let's say the location he's needing to scout is a fort. He eventually gets there, sees what enemies are about, and immediately leaves. He may be detected....that's okay. As long as he escapes and can make a note of it, he's done his job.
After The Scout returns to wherever he was last camped at, Character #1 now has the information he or she needs to advance into that fort, or not advance into it. It's my way of keeping my dead-is-dead characters alive, like I said.
I'm also picturing the Scout as being someone who's able to hunt and live off the land. There's lots more harmless wildlife in vanilla Skyrim (compared to Oblivion) and The Scout will be able to live off of this. He'll definitely carry a bow and a daggar.
Stay tuned for another idea I've had: The Witch!