In reply to Roberttaylor:
Not an easy answer as there are quite a few variables to consider - eg. are you going to be swinging leads with someone and so you won't need so many yourself as you'll be able to share? If you're going to be doing all the leading then you'll obviously need more.
The following is just my opinion (based on 16 ice climbing trips to France (mainly Ecrins) but also to Norway and Italy and climbing up to WI5):
Generally speaking, all running protection in the Ecrins is on screws (although very occasionally you can use a tape on a tree or come across a bolt/ peg runner.) Belays are often bolted (although these can be buried.) Trees are often used for belays too but you'll also need to be prepared to belay on screws, even on popular climbs if the belay bolts are in use by another party or if climbing something less popular or esoteric. Sometimes two consecutive belays can be on screws. If the ice is poor, you can easily use up three screws while 'manufacturing' a good belay. Pitches can also be close to 60m in length on many routes.
So you need to be prepared for two consecutive belays on screws - 4 screws minimum. Then, if climbing long pitches, you may need anything between 6-8 screws as a minimum, depending on how hard it is, how easy it is to place screws or how prepared you are to run things out.
So, a team will ideally need between 10 - 12 screws - and on quite a few routes 12 won't feel like too many! If these can be bought between 2 people, then so much the better.
As for lengths, I tend to carry a single 22cm (mainly for belaying and Abalakovs), then the rest are all 16cm together with a token 13cm usually carried as an 'extra'. (I have 10cm screws but have never placed a single one in continental ice.)
HTH.
Dave