In reply to Tim Chappell: You can go up Gran paradiso very easily via the Normal Route solo without crossing any glacier. You can see crevasses about but you're not anywhere near them. We went up ropeless last August and it's just a walk with a wee scramble at the top. Nice though.
Remember there's plenty of peaks below 4000m that are nice too and don't involve glaciers. We are in Termignon at the moment and had the intention of going up the Dent Parachee and Grand Casse (though we'd use a rope for this)
We're having van issues at the moment though and aren't able to get much of anything done as we're busy with garages
Also, we went up the Balfrin last summer (just under 4000m) and that didn't involve glaciers (you go up some ridge in it's entirety, bit chossy at bottom but it means you skip the glacier crossing) sorry can't remember what ridge it was, but will be in my log book.
Also, the Laginhorn but i think someone mentioned that already. We were also going to do some long traverse of the Weismiss that involved missing out the glacier, but can't remember what it was either! (it's in the Valais East guide though)