I have found two interesting challenges are to collect all of the Dragon Priest masks and to get all the Daedric artifacts. Both will involves you in a very varied and often unusual tasks.
Thanks, sounds challenging I have only one mask at the moment and what are these 'artifacts'? I don't understand them or what they are.
Lovely weapons, armor, and things like Azura's Star (Black star) that are rewarded to you when completing a quest from a Daedric Prince.
Examples, you get Clavicus Vile's masque through his quest, initiated in Falkreath by finding a dog for Lod.
Merhunes Dagon (started after level 20 by getting an invitation to the Dawnstar museum), Molag Bal (House of Horrors started in Markarth) and Mephala (Dragonsreach in Whiterun) all give you weapons.
Boethiah (After level 32 I think you will start to see followers of Boethiah and this will initiate it) gives you armor, etc etc etc.
If you're not into enchanting and don't want to work on it, then you should definitely seek these out. They have decent to strong enchantments and are unique.
Oh, and Azura's Star works wonders for increasing enchanting. Just get a weapon with soul trap, and every time it sends a soul into Azura's star, use the star to recharge your weapon. Rinse repeat and watch that skill rise easily to the 40's, then starts taking a little while, but still decent. To start this quest, ask at the Inn for rumors in Winterhold, and she will eventually mention Azura's shrine. Or you can just go find the shrine, there is no level requirement.
There is also no level requirement for the House of Horrors through Molag Bal.
You can also get an interesting staff from the lovely mad prince Sheogorath, this is initiated in Solitude through a beggar in the streets talking crazy about his master missing (you can just run into him or hear about him through rumors in the Solitude Inn) Not sure the level requirement for this one.
You also can get another reward through... ugh... I think it is Sanguine? Can't remember. But it's called "A Night to Remember" and I also can't remember the level requirement for this one, I think it might be around 20. This can be initiated through any Inn/bar throughout Skyrim, whether that be Whiterun (typically here) or Solitude. A man named Sam G will invite you to a drinking contest. Very fun quest, definitely do this one.
Peryite, go and find his shrine (google the location) and you will find a Khajiit there, then your quest shall begin.
Meridia, through finding Meridia's beacon in random loot, and it will begin as she will speak to you.
Namira is quite an interesting and slightly disturbing quest. Go to Markarth and enter the keep there, and as you head for the Jarl in the back, you will run across the priest arguing with a nord about the Hall of the Dead located there. Speak to the priest and persuade him to let you help him. Go into the Hall of the Dead and search around, then it begins.
Then there is Vaermina, initiated in Dawnstar I believe. Just ask around about the nightmares people are having and go into the Inn there, and speak to the male priest about it. It shall begin here, this is also interesting.
Anyhow, sorry for any spelling mistakes. But these Daedric quests should definitely keep you occupied, and they are all very rewarding and fun. I think most of these have some form of level requirement, but I know for sure that Molag Bal's house of horrors and Azura's star does not. Good luck to you!
Can you tell yet that the Daedric quests are my favorite?