I walked west and south from the opening area, happening upon wolves that I tried to defeat with a sword and shield, but couldn't. So I switched to magic, sneaking and a bow and got past them, happening upon a magic Word and a small building filled with vampires. Their leader managed to curse me with vampirism, but I wasn't aware of it for a while, I just kept walking and exploring. Finding a sort of wooden atronach in a circular ruin that kept chasing me, I ran for many miles while dual wielding a healing spell. I excavated a tomb. I got chased by regenerating trolls I couldn't damage fast enough to kill over snowy mountains and the ruins of Labyrinthian. I walked out of the world during a glitch, allowing me to come back into the world at the top of stairs guarded by tons of necromancers and sneaking past them all, which meant i was free to walk into their den, open a chest and promptly fall three floors into a cell. Their leader talked a big game at me, but he regretted having his back turned when I got the lock open and started bludgeoning him with a warhammer I had just found. I talked with a convicted child murderer who was a werewolf, and when he escaped from prison I chased him to Bloated Man's Grotto and killed him. I headed for dawnstar to find the hilariously named Rustleif that i had seen in a screenshot, then found a stranded ship on the coast and a grotto called Yngvild full of ghosts on an island. Then the vampirism kicked in, people started fearing me and I could not figure out how to cure myself.
So I looked up a guide, and it said: You're too late to cure it conventionally now that it's advanced this far. Get to this town, which is troubled by the death of a family in a mysterious fire. Solve that mystery. Then talk to this guy. If you have a soul geam, he will transfer your curse to that gem.
I had no soul gem, and no way to fill it, but one of the places to get one? Whiterun, where the main quest had pointed me to since forever. So I walked there, drinking the blood of sleeping people to appear inconspicous. I listened to the jarl, but not really. Then I talked to his mage, and I bought the Soul Trap spell from him along with a gem. After which I went north to that sunken ship, cast the spill, Killed some wolves and trapped them in the gem. Went to the town, started the ritual, and then I was cured. So I decided I should _probably_ do some kind of quests instead of just wandering around for 20 hours. I went to the College of Winterhold since they probably had some more magic for me, and the quests in that storyline were all uninteresting, but they gave me a goal to work toward and new reasons to explore the world to reach the marker. So I bought a horse and beat a lone necromancer up to no good on a small mountain northeast of Whiterun. A horse which then died off-screen in mysterious circumstances when Winterhold was invaded by Magic Anomalies. I entered a Dwarven ruin and discovered it was full of this world's equivalent of the LotR ORCS, and spent the next hours running, sneaking and arching to get past dudes that could beat me in a few hits and vastly outnumbered me, my fireball spell, by bow and my two-handed warhammer of embers. I let one of my classmates practice her spells on me and then join me on my journey, a 17-year old sounding, 90-year old-looking woman named Brelyna. Another gave me an exploding flame cloak that damaged me, but did wonders against the skeletons and zombie dragon I soon ran into. I encountered two dragon priest, one on the top of a mountain that I dueled with very boringly for an in-game day, going left and right while shooting our one spell at one another. The other was found in Labyrinthian guarding the Staff of Magnus, which is also a funny name, and with it I saved the college and became the principal.
Very aware of my new responsibilities, I put on the principal's robes, took Brelyna with me and legged it for the southeastern borders of Skyrim, where there were lots of places I hadn't been yet. And that's where I am now, after having beaten another dragon priest in a cloister and beaten a LOT of necromancers and bandits and bears. Also, helping a daedric lady beat a very mean sorceror who locked himself in a special soul gem of hers to live forever.
I don't want to do quests, other than what I run into. They turn the game into a chore, like Kingdoms of Amalur or something. The exploration keeps me going. I love it. Skyrim seems to be better for it. I have seen NO dragons since the opening, and I bet if I don't progress the story they will never start bothering people.