I like that in Skyrim each dungeon gets marked as complete once it's done. I think each dungeon should have a boss, and each boss should have some kind of unique item. So there is always an incentive to dungeon crawl because you can't craft those items.
Also for every chest (maybe only every locked chest) there is a tiny chance of something really good. To encourage searching everything. The word walls in Skyrim are a simlar idea and they are effective.
Some kind of system for making use of stuff you pick up: if you can't carry it you should be able to at least break it down and use it for repairs or something.
And it'd be great to be able to go to an inventory or container item and choose 'send to my follower for selling asap' and also 'send to my follower to keep.' Followers would excuse themselves in towns and take care of business (e.g. selling stuff for you, picking up food, arrows, etc).
I'd like some weird environments with a non-earthly look. Some oblivion plane stuff too: I liked these in TESIV (even though they were very similar). I want some Ayleid ruins, quests. Also some regions that are just idyllic and beautiful. Fields of flowers like in Oblivion, that autumnal look of Riften, etc. A really tall mountain / cliff ala Dive Rock.
In general, close attention to the UI to make sure it's efficient: we play these games for hundreds of hours so every unnecessary click adds up.
Let us make an unarmed character who has a viable progression. ie a boxer. Nothing over the top: just let unarmed scale with level with comparable perks.
Make sure we can place items and have them stay there. Hearthfire style house customisation in DLC is fine but make sure even the first houses have places to put my stuff. Good bookshelves. I want to be able to collect diamonds and make a pile of them.
Economy: make it viable to (for example) hunt animals or brew potions for a living.
Save files grouped by character please.
Bring back custom spells please.
To encourage interesting solutions to problems let us raise dead creatures, paralyse people and creatures, freeze, transmorph, make things weightless, frenzy, detect life, levitate, recall, poison, heal others, charm, terrify, turn.
Stats please as a starting point and then make levelling based on actual use (ie like skyrim w/ stats). I would like to have an intelligent character with low charisma, for example. I think you should get x points and choose how to allocate them.
Let us wear more than two rings but scale back the effect for each additional one. I think this could be cool: what if there were a set of four rings, and if you find all four and wear them it has some unique effect?
Make mage spells etc feel impressive and powerful.
I liked the mage's guild line in oblivion: it seemed much longer than that of Skyrim. Also it had that initial requirement of getting letters of recommendation. Every guild should have some kind of entry requirement. The DB line in Skyrim is a good example: you need to actively seek entry, not just show up (ok not many guilds are weak, but the skyrim mage's guild seemed too easy to join).