I only wear clothing, no armor, no skill enchants (fortify one-hand etc... ) I never fast travel, I mainly use a bow but will fall back to useing daggers if the baddie gets in too close, do not use magic what so ever!! While I'm on the road I try and make it to my destination by nightfall but if I cannot make it then I push for the nearest town with an inn to stop for a bite to eat and a bed to sleep in till the crack of dawn( I always wake up by 5:30am-6 ). I walk every where unless running is a priority( like runnen from a dragon ) and I ALWAYS hide the bodies of those I have slain.

I restrict all my characters. This latest is an interesting one... I'm not using merchants other than the few merchants available in the orc outposts. I'm also not using enchanting, as it seems orcs don't do that kind of thing (no tables at all in the outposts). So no purchaced magic items at all, and very little cash to be made by selling. I also only use fast travel for truely tedious treks, like that up the 7000 steps and back.

I was going to say no housing either, but caved on that one.

I've set a goal to be the Thane of every region as I pretty much ignored that aspect of the game in my previous three characters.

Got a few "basic" restrictions, like no abusing glitches and whatnot.

I restrict my characters from being restricted by anything.

Lol no, I am dragon born, strong as a warrior, devious as a theif, and adept in the realm of magic.
just like being the champion in oblivion. now sure, as all people, i am better at using the 1 handed swords or bow and arrows, but i can do it all.

I play with a bunch of restrictions. For starters, no fast travel on any of my characters and I typically turn the HUD off entirely.

I also try to remember to sleep and eat regularly, but I am not anol about it. It is just fun to hang out in taverns and relax every once in a while. I never get tired of listening to the minstral in the Whiterun bar playing Ragnar the Red. The last line in that song always makes me laugh.

As far as character specific restrictions, I have the following

I have a Nord warrior who casts no spells, not even healing. The Nord does not do enchanting either. He is a very anti-magic warrior.

I have a Dunmer nightblade who uses no weapons other than bound weapons.

I have a Khajiit archer who uses no melee weapons, only bows and claws. He also only enters walled cities after dark and wears a hood and robes when he does to hide his race.

All of my restrictions are for roleplaying/immersion purposes, not necessarily to make the game harder (although many of my restrictions do end up having that effect).

Sometimes, albeit minor things.

My mage hasn't done any of the main quest because I feel she's unprepared for dragon attacks. Even as a level 20, my main magic rotation is flames+firebolt. It'll get better when I get better equipment.

The same character may not bother with a couple of the factions, though I may find myself doing the Dark Brotherhood anyway (It's fun!)... Though I'm fairly confident that she'll never bother with the Civil War at all.