The first thing I did was chop wood to get gold actually, it was boring work but it gave me a nice little start with the Gold it generated. Plus I was following a guide on how to create a 'god-class' armour and weapon set, and that was the first step.
The first thing I did was I tried to kill Ralof. Yes. But unfortunately you can't kill him because you'll get your quests from him in the first part so after I beat him up and realized I can't win I ran away and just started a new life away from Riverwood.
In my first game, I was pretty by-the-book. Whatever the story hinted at, I did it. It got me pretty far. So yes, the whole Windhelm, became a Companion, helped the Jarl, became a Thane, became a Rogue... It was epic, but then interest faded. Then about two years later, I restarted and things somehow didn't go the same way. Probably because of some of the mods I had.
I killed a chicken in Riverun. Suddenly the whole town started attacking me for my crime. It was hilarious.
Dungeons and caves, mostly. Dwemer ruins, Nordic ruins. Then again, I didn't really go out looking for them, I just did whatever was along the way for whatever quest I was doing. Of course, that usually resulted in me filling up my inventory extremely quickly and having to double back to the nearest town... I can just never resist.
The first thing I did before any missions was just exploring around. I enjoyed the vastness of the map and really enjoyed the scenery at first. It was unlike anything else I had ever seen in a game before.
Maybe it will sound a little weird, but I started to check if there is another way to do the first mission. I just wanted to be sure that I discovered everything at introduction (playable part).
I probably went hunting or started collecting alchemy ingredients. Poison archers are one of my favorite ways to play the game and its actually kind of hard at the beginning while your alchemy skill is low. Raising it and Archery were probably the first two things I did.
First thing I did once I got out of the cave was head to Riverwood, (I think that's is what it is called) and bought a few supplies and then went hunting for deer. I wanted to increase my archery skill rank as quick as possible. Then I met by first mammoth and died a glorious death. Good times!
From watching a bunch of gameplay footage, the first thing I did was go become a companion and then become a werewolf. Because werewolves are cool.
Like other posters, the first thing I did was explore and get used to the game, controls, etc. I'm still a newer player so I'm not really well versed in anything yet, but I'm having fun doing the side missions and enjoying the cities.
I don't remember too clearly, but I'm pretty sure I just did what I normally do when playing new games--that is to say that I went and explored the world. It was pretty incredible, too, but I probably got lost a fair bit, and I'm pretty sure I somehow wound up dead a few times.
The first thing I did in Skyrim was find some poor sucker and kill them, then go to sleep and wake up with a creepy message, then join the Dark Brotherhood... And completely ignore the rest of the game xD
I picked flowers, and caught a couple of butterflies. Yep, that's how I started the game off. Hehe. After that I followed various quest lines, and snaked into the mine that's close to the first village. It's a nice little mine and helps you get a bit of experience, as well as some much needed gear and ore.
On my way to Riverwood I picked flowers(as most of us did). Then I decided to help Faendal in Riverwood and recruited him as a follower. I just didn't like Sven that much. I also did The Golden Claw quest to get things started.
I may have made a save and then went wild and tried killing all of the residents of Riverwood. I may have gotten killed after that. I may have reloaded about a dozen times trying the same thing...
