Thanks Odile for plugging my blog, and to Retiredin NH for re-plugging the plug

. More ideas (in French) on
http://www.hikr.org/user/stephen/tour/
Kristanez - the Tour du Mont Blanc mentioned above is a must-do and is not difficult at all, but you need two weeks to do the whole thing. I was sceptical because it has the reputation of being crowded, but if you aim for end of August/early September you will be OK. The scenery is stunning and incredibly varied.
In five days you could do the Tour des Muverans (see
http://www.hikr.org/tour/post14721.html) starting and finishing at Ovronnaz, Derborence or Pont de Nant. It's quite physical but worth every drop of sweat, you hardly see a road or a village for the whole five days.
You could do a week along the Alpine Pass Route (though the whole thing needs two to three weeks), some of the stages are long but there are almost always transport options if you need to shorten a day. See the blog that RetiredinNH has linked to, under July 2010.
In four days you could do the tour des Dents du Midi (see
http://www.hikr.org/tour/post7162.html), again worth the effort and off the beaten track.
In ten days you could do Chamonix-Zermatt, or its shorter variant Verbier-Zermatt in seven days... I don't have a description of this one online but have done it and can guarantee that it's worth it. Probably the most difficult of the hikes mentioned here.
All of these are on well signposted paths and don't require a guide, assuming you have a minimum of mountain hiking experience and physical condition. They can all be done with guides and trekking agencies as well though - this is how I did the tour du Mont Blanc and Verbier-Zermatt.
Edit on hut bookings: yes, you should always book ahead if possible, the hut wardens need to know how many people to prepare the evening meal for. On Saturday evenings even in September, huts get very crowded and you should book several days in advance. On very popular routes like the TMB and Chamonix-Zermatt, it may be best to book several weeks ahead at least for the Saturday night. You can always call the hut to cancel if your plans change.