I've always saved in a new slot. Never understood why I should scroll down and choose an old one, when it's easier to just click where I am and create a new. And considering how buggy this game can be, it has turned out to be a good practice.
When I was on PS3, I simply cleared out most of the old saves when the memory was full. Not sure how many slots are allowed, it might depend on the size of the save too (?), but well over 100 - maybe even 200? Don't remember.
Now I just delete the old saves every now and then, when I feel they are too many. I usually keep the last ten or so saves (I save OFTEN so those ten saves might very well cover a single quest), and for nostalgic reasons I like to keep the very first save after character creation as well. When I retire a character, I usually keep the first and the last save - before I started my last playthrough I wiped the saves folder clean though. I changed so many mods that those saves would most likely be broken anyway.
Edit: I don't know how easy this is on Xbox, but on PS3 I had created separate users for my different characters. Not the account itself, just a new profile. That way it was very easy to keep different saves apart, since I could never load (or overwrite) the wrong save. Plus, I got all the available save slots for each character! ![:)](http://www.gamesas.com/images/smilie/smile.png)
(On PC, I use a savegame manager to keep the characters apart.)