I myself like to change my character every 20 levels, making my character older every time.
It's a fun way to play (like earning a badge for reaching the next stage) and helps you immerse yourself in the game in my opinion.
By the beginning, my character has short hair, a clean shave and very scrawny with light skin.
By the end, my character is a bit more buff, and he is old and looks very similar to Gandalf. He could easily be mistaken for a Greybeard at that point.
During the level 41-60 period, I decide to give him a scar to make him a bit more authentic. After all, Skyrim is no "Hello Kitty Island Adventure"
Anyways, let me know about your ideas.