I've become prone to deleting characters and starting a new one due to boredom. Any suggestions for a fun character build I could try?

How about a pure thief who never kills anything? Sounds boring, but it's tons of fun and forces you to play in a new way. Practice that sneak!

Just getting into the Thieves Guild the first time without killing is a challenge

A nvde Nordic Warrior who was fooled by Witches?

I'm playing a heavily-armoured (occasionally mounted) archer at the moment. So much fun.

Especially when you pull off trick shots. For example, there was this bandit who'd attacked my follower, Faendal, and caused him to start bleeding out. And unfortunately, the bandit kept moving around, so I couldn't shoot him safely without the risk of killing Faendal.

That's when my trigger-finger got sore. So I unclicked the mouse, and I let an arrow fly, and the kill-cam started up. The arrow missed Faendal's shoulder by less than an inch, and flew right into the bandit's neck.

So, my advice? Play. An. Archer.

This.

The most fun character I've played.

http://theskyrimblog.ning.com/group/character-building

Only use shouts to kill.

Get big bounty on your head in every city, live and survive out in the wilds like a true ranger.