Leave a Nord mead and a flower on the corpses of friendly npcs who recently died in the game (not with skeletons or so).
Fight enemies with the "appropriate" arrows: falmer with arrows made by their archenemies the dwemer, dragons with ancient nord arrows, draugr with ancient nord arrows (because they're undead who're supposed to go into eternal rest already; like their own kind telling them they don't need to guard the tomb anymore), and so on.
Being overly empathic with dragons (at least with this character) and using invisibility potions when visiting a lair with a power word, so the dragon doesn't see me and doesn't get disturbed. (it's part of character development 'though, before she met P'nax she slaughtered every one of them ... she still killed one elder dragon in his lair after the meeting, but suddenly felt terrible about it, went to P'nax to meditate about it and went back to leave flowers and "food" (aka gemstones) in the treasure box (never looted the box either))
Fight wild animals with her fists, so the battle is kinda "fair".
She never uses soul entrapment magic. She does however use up the filled soul gems, so the souls get freed. There are quite a lot of them to be found in the game, and they weigh a lot too.

Only use shouts with dragons and draugr. She follows the Way Of The Voice.
I always leave the money in the Burial Urns. I shall not touch the alms! Potions on the other hand ... The dead can't drink anyway.
I always remove Centurion Cores from the Centurions, and hide them on a good distance from the machine. So nobody would get the stupid idea of 'reviving' a Centurion again. Only time I didn't do it was during the quest in the dwemer ruins below Markarth, because I left it alive (for obvious reasons if you followed the quest well).
Dangerous but interesting quest materials concerning the main quest are stashed in the chest in Breezehome, weapons are stocked in a dresser with a weapon plaque and hunter's bow above it, armor in a dresser not far from that one, clothes and other disguise material in the wardrobe in my room, and so on. Notes, diaries and books which I don't need anymore, or which are deemed too dangerous to the disposition of my character get tossed in the fire of Breezehome.
I'm also hoarding books. I'm trying to collect books which can function as an introduction to the Skyrim country (books about the holds, ...), books which contain information about the main quest and civil quest (books with information about the Aldmeri Dominion, The Great War, The Bear Of Markath and so on), books concerning the political works as my character will get in touch with that anyway (The Wolf Queen & The Real Barenziah collections), and simply romans which are neat to read (Immortal Blood, Wraith's Wedding Dowry, ...)
There's also an ancient Nord ruin somewhere populated with bandits (and draugr further on), who seemed to have had a drinking fest. The whole ruin was littered with empty wine bottles and so on. Being the respectful Nord towards ancestors, I decided to clean the place up and drop all the litter in the pockets of the bandits. It was a ruin with a door which requires a key, so I assume it's a quest-related ruin. Must've been somewhere in the Reach I believe.
My character isn't all that comfortable with the extortion methods of the Thieves' Guild (but she joined so she could become head and reform it), so every time she extorts by breaking things, or steals something, she puts something of equal value in the place. Unfortunately, you can't take a dwemer urn from a ruin with you for some reason, so I decided to get a whole tableware set with bowls included and 'sell' (read: give) it to the shopkeep after selling him enough stuff so he has 0 gold.
Oh yeah, and that "punishment" you got as a quest for the Dibella temple? I did it completely naked (aside from my weapons) and with a Dibella amulet on. It was kinda hard to fight all those forsworn without armor, I really had to rely heavily on my sneak skill.
On that same note, I always wear my Amulet Of Mara when doing a quest for the that divine.
I also always try to cover my tracks when "invading" enemy territory. I hide corpses in dark corners, or throw them in the water/from a cliff so it looks like an accident. After retrieving my arrows of course.
Oh, and every now and then I just HAVE to jump or whirlwind sprint off a high mountain or cliff - just to watch my heavily-armoured Orc warrior fall and tumble down the mountainside like a ragdoll. Also, I sometimes jump off the College bridge just to see if I can hit water when I land and survive. I usually don't.
I do that too. I always try to fall as long as possible. Tried it at High Hrothgar several times - both at the Greybeards' HQ and at P'nax' place- but it is what it is, a mountain. meaning no steep cliffs, and no long falls. Kinda disappointing. Best jump I had until now was the Bard's Leap, unfortunately.