Awesome; self-indulgent wall-of-text time!
My restrictions are primarily moral ones, but I've also recently adopted gameplay restrictions, which have only helped make things more immersive and fun.
None of my characters steal or murder as a general rule, and I'll go out of my way to see that I do not have to do either. If I have to take something, there had better be a good reason, and if I have to kill someone, there had also better be a good reason, or I'll look for loopholes and ways out. Killing hostiles or looting dead hostiles is one thing, but killing someone because I don't care for their attitude or getting sticky fingers in someone's shop is quite another. So, generally I try to be altruistic--help the innocent, bulldoze the wicked, or thereabouts. If I have to do something dicey because there's absolutely no way around it, I'll RP it so it can at least be explained away; the only instance of this I've as of yet run into is killing Grelod in order to wipe out (the majority of) the Dark Brotherhood (my character goes to the Orphanage after hearing about the conditions from Aventus, overhears Grelod being verbally abusive towards the kids, pokes around, sees the shackles, talks to the children and hears the stories of abuse, loses it, and waits for the kids to go out to play before drawing his/her weapon and making a mizzle of the old hag's blood. A good deal of time is spent at Mara's temple in shocked reflection after this).
As for gameplay, it depends also on the character. Narienne, my female Altmer spellsword, uses skill and sorcery to dispatch foes, not relying on brute force or intimidation. She does not choose to threaten enemies, takes care to be especially stealthy, and does not ever use shields, dual wield, or shoot bows. This is because I want her to be primarily a spellsword, not a ranger or a warrior, and I RP it as her suffering from an improperly healed shoulder injury which causes her too much discomfort to use anything more than a spell in her offhand. She only ever uses magic in her left hand, and only ever a sword in her right, as I consider other weapons not proper for an Altmer lady (though I'd make an exception for a dagger), though I am considering letting her use a crossbow as a longbow alternative; the slow reload time would be accounted for by her shoulder injury, which renders a crossbow the only potential ranged weapon she can comfortably employ. She only uses light armor, of course, and prefers circlets to helms and gloves to bracers--and prefers to destroy or significantly weaken enemies with spells before they get within sword range. An ex-Thalmor, she can handle a blade well enough, but knows the value of a good spell for those who are not musclebound meat grinders.
Speaking of musclebound meat grinders, Ulfius the Iron is my Nord warrior reboot. Much more of an in-game avatar of myself, Ulfius prefers to intimidate hostiles or give them the sharp edge of his war axe if they presume to do more than posture and sputter. An ex-legionnaire, Ulfius prefers to be in the thick of the melee, axe swinging and enemies falling, with only a stout iron shield in his left hand (maybe I'll play with dual wielding with this character more--just didn't feel right with Narienne) and fire in his eyes. He might use swords or two-handed weapons from time to time (and probably just to give his shield arm a break on occasion), but being the born-again Nord patriot he has become since just prior to his near-death at Helgen, the deep cultural symbolism of the mighty war axe compels him to take only that as his weapon. However, Ulfius will not hesitate to pull out a bow if needed, having learned well the power of a nocked shaft against distant foes whilst serving in the Legion. He uses healing spells, scorning offensive magic as somewhat cowardly, though the ability to magically summon a weapon in case he is disarmed or the ability to temporarily augment his armor is very appealing. Ulfius wears only heavy armor or a mix that primarily favors heavy armor, and has been conditioned enough in the Legion to wear it for days on end; to Ulfius, iron and steel are like hide and leather.
Both characters use Shouts; Narienne despite her persistent dumbfoundedness that she is the Dragonborn of the Nord people, Ulfius in excited awe of the same. Neither use Soul Tear, or for that matter, any form of necromancy besides.
Both of these are infinitely more restricted than previous characters in a TES game or another game, where I was always did what I liked and only held to moral restrictions. But, these have been the most rewarding and enjoyable characters I've ever played, and in large part, it's due to the restrictions I've placed on them.