I have so many characters that it's stupid and they each serve their own purpose. One character I have for the sole purpose of uber-leveling him to the point of godhood. He's a Nord and I used the Conan the Barbarian formula that is all over the web. I named him King Conan and he specializes in, well, everything. He is Dragonborn, sublime thief, master assassin, seasoned warrior, and a mighty mage to boot. I know Conan never used magic but that's not the point. I use him for nothing more than the thrill of power leveling and smashing my enemies by any means that strikes my fancy. Once I get him to level 100, I'm going to use my contact in Riften to change his face and make him appear older with wrinkles and gray hair. When all is said and done, he'll have more money than the Empire, a house in every available location, and treasure out the wazoo. Why? Because Conan, that's why.
And then I have a few character who I've made for various purposes of making the game more challenging beyond just raising the difficulty. Like gimping, I suppose. Some rules I like to abide by are those like No Gold (I can collect all the gold I want but I can't use it to buy anything and so any potions I use I must make or find and the same goes for armor and weapons) and then I even have some more strict rules such as my orc who I will not allow to loot armor from anyone who is not a Nord, Imperial, or another orc. After all, how would heavy armor on a wood elf fit on an orc? I even have a mage whom I've determined has a phobia of "medicine" and so she refuses to drink potions and can only recover health by eating food (she also does not eat alchemical ingredients and so I've taken to referring to this as the Glutton rule). Needless to say, she does a lot of cooking as you'd be surprised by some of the benefits you can get from prepared meals such as veggie soup. I even have a high elf who focuses on two-handed, alteration (no armor), conjuration, and enchanting (needless to say, he does a lot of prep before battle). One of his preps is that he NEVER goes in to battle without first consuming alcohol and the only way he ever recovers fatigue is by consuming more alcohol. Needless to say he goes through a lot as swinging that giant hammer really wears him down and the side-effect of alcohol is crappy stamina regeneration. At first I called him a Drunken Hammer Mage but now I've taken to just calling him my Hammered Mage. Most of these characters though are optimized for the purposes of making the game more challenging and so I have to approach each one with strategy in mind as opposed to playing to my favorite skills.
And then I have those character whom I straight role play with. Making the game more or less challenging comes and goes depending on the character as I never "gimp" myself for purposes of gameplay but rather play my character a certain way based on the story I've built for them. Such as my "paladin" who despises the undead and has a fascination with the dwemer so she collects everything she can from books to artifacts and even random junk. She has even taken up smithing on the side in the hopes that she will some day be able to make (and enchant) her own dwemer armor. I follow a few rules to make them game more "realistic" but I don't go to the extreme. I limit my fast travel use but will never opt out of it completely. It really comes down to on-the-moment judgement calls. As a paladin, she uses a mace, a shield, heavy armor, and restoration spells to heal and repel undead. She also uses conjuration but never raises an undead or summons a dremora but rather sticks to the three atronachs (usually the fire atronach). But when she is exploring dwemer ruins (it's her "hobby"), she replaces her mace and shield with a two-handed warhammer and her trusty crossbow.
Last but not least, I have a few character whom I've made based off of some of my favorite characters found in fiction. So far I only have three and they call come from the mind of R.A. Salvatore. Obould Many-Arrows (an orc king), Harkle Harpell (a werewolf-wizard), and Artemis Entreri (a master assassin with an enchanted, life-stealing dagger). I just wish there was a way to work his magical crown in there which is able to shoot fireballs. I've been considering making a certain famous archer......
*takes a breath* And I'm done!