There is a dearth of decent fabric shops in Geneva (or, at least, I haven't found any good ones yet that are affordable...), so these are some of my sources for my sewing needs. I'm currently investigating the various shops in Geneva (and Lyon), so will post my findings at some point soon!
I have many more places bookmarked than given below, but these are the shops I have used and would recommend (no commission for me, I just had good experiences!), I want to try, or have been recommended to me. (At some point I might add a round-up of all my bookmarks for my reference.) I haven't tried those in italics, and any opinion and information given is based on their website, window display, or recommendation... :) Of course, there is also eBay in general, but not everyone will ship to Switzerland.
Thread and Needles (a French-language sewing forum), has information on fabric and notion stores in Switzerland, plus nearby areas of France for those in Suisse Romande.
Geneva/Swiss shop reviews
Manor: Swiss based department stores. The larger stores have pretty good haberdashery and notions, plus yarn (I go to the main branch in Geneva). They often have reasonable deals during sales periods (I recently stocked up on serger thread at 5CHF per cone - well, that's cheap for Switzerland).
Coop: Some of the larger Coops have yarn and haberdashery. I got to Coop Cité Fusterie, and there's often a wider range of yarn, but I prefer Manor for haberdashery. Coop only sells interchangeable circular knitting needles in wood, Manor only sells fixed length in both bamboo and metal.
Mercerie de la Madeleine: Haberdasher in Geneva. A good range of all sorts of haberdashery and notions, plus some lining fabric. Moderately expensive.
Bernina: Bernina franchise with shops in Sion, Martigny and Geneva (I have only been to the one in Geneva). Some quilting fabric, but most useful for threads, especially serger thread, including woolly thread. And of course sewing machines (I bought my serger here). Beware, it's Swiss prices though, I definitely paid well over the odds for my serger.
A Gras: Fabric shop in Geneva (the fabrics sold per metre are in the back of the shop). A big range of fabric, but eye-wateringly expensive. The cheapest I found was plain silk charmeuse at 44CHF per metre, but most prices seem to be in the range of 70-150CHF per metre. Ouch.
Pompon: Shop based in Zürich with an online storefront too. Looks like a really good range of fabrics, but since the web shop isn't working right for me I can't tell whether the prices are for whole or half metres (I suspect the latter unfortunately) - I plan to drop by next time I'm in Zürich though. They also have a sewing space available for use, and hold classes (and not just beginner classes).
Au coeur du patchwork: Shop in Nyon specialising in quilting supplies.
ALJA: Swiss chain of fabric and yarn shops, also have online shop. Prices vary between not too expensive and crazy expensive.
Textiles Acacias: Geneva.
Mercerie & Tissus: Geneva.
Online-only Swiss shops
Busy Needle Quilting: Offers machine and hand quilting services, plus lessons. Also stocks batting at pretty good prices.
Stoff & Kram: Fabric is fairly expensive (the prices are by the half metre), but seems to be all organic cotton. Lots of cute ribbons and bias trim (although seem to be out of stock quite frequently).
Grüne Meter: Again, fairly pricey, but all organic.
Y'a matières: Expensive!
Snowflakes Fabric: This Swiss-based Etsy shop has lovely quilting cottons at very good prices, but a very limited stock.
Tissu & Co: Swiss online shopping, but have yet to try it. Looks like a nice selection of interesting fabrics (plus some haberdashery), but again on the expensive side - with all these online Swiss-based shops, I'd need to weigh up how much imported fabric would cost in customs fees for an equivalent when buying.
Mondial Tissus, Annemasse: French chain store, also have branches in Lyon and Annecy.
Lyon: Lyon has a history of fabric production and it's been somewhere I've been meaning to go for ages. The website linked has a good list of places to shop! Now I just need the works on the fast train line to be completed...
Paris: There's some super fabric and haberdashery shops in Paris (and only 3h by train from Geneva). Melissa's guide (linked) is very useful. Most shops are around Montmartre area.
Goldhawk Road, London: Not online, but very definitely worth a trip if you are near London (this was where I shopped when I lived in London). My favourite shops are A-One Fabrics and Classic Textiles. There are also more fabric and haberdashery stalls in Shepherd's Bush Market.
Online: mostly fabrics
Fabric.com: US based, and the site I've shopped from most in the past. A huge range of discounted and reasonably priced fabric, particularly good for basics. Prompt and fairly reasonably priced shipping to Europe. Frequent sales and coupon codes. Edit (mid-2012): I've been having a lot of problems with delays and stock level accuracy recently with Fabric.com. Apparently this has been due to a move of warehouse and stocktaking method, but I'm very wary at the moment. Edit (late-2014): the delays and stock problems have resolved themselves, although the average shipping time has increased (they've got rid of their 24hr turnaround promise). It's shipped UPS though, so once it has been shipped it takes only a couple of days to arrive.
eQuilter: US site. Huge range of novelty quilting weight cottons and quilt supplies, plus occasionally a few other fabrics, very reasonable shipping to Europe. Cost per metre is more than Fabric.com, but shipping is much less.
Gorgeous Fabrics: US based. Many high quality and designer fabrics, often relatively small quantities available so be quick...
Thai Silks: US based. A huge range of plain and printed silks of various weaves and weights, including silk for painting.
Spoonflower: Custom print your own fabric. I've never actually tried this out, but it's a really cool idea. They keep expanding the fabric selection too. It's pretty expensive, but for something special it could be really useful.
Emma One Sock: US based. Designer fabrics.
Online: mostly notions and supplies
Sewy.de: German based (website in German only). Supplies for making lingerie and swimwear, including fabric and patterns.
Fashion Sewing Supply (Sew Exciting): US based. High quality interfacings.
Bra Makers' Supply: Canada based. Fabrics, notions and patterns for lingerie and swimwear. Shipping to Europe can take a long time.
Hamon: France based, with a shop in Paris, plus mail-order online. Various sewing and pattern-making related supplies and haberdashery.
MacCulloch and Wallis: UK based, shop in London. Great for haberdashery, but the fabric is very expensive. They do mail order (although I've yet to check if they ship to Europe), but if you are in London I would highly recommend a trip to the shop, I could spend hours (and a fortune) in there.
Morplan: UK based, with a shop in central London. All sorts of notions and supplies for everything from pattern-making to retail. Mail order as well, but I have yet to check if they ship to Europe.
Kleins: UK based, with a shop in Soho, London. Suppliers of haberdashery and notions, with a huge range, especially for boning and corsetry supplies. They do mail order, but unfortunately only ship to the UK.
Online: mostly patterns
SewingPatterns.com: US based. Discounted sewing patterns, including many that you can download and print at home (great to save on postage or time...). Frequent sales - I only buy from Annoyingly sometimes needed to be prompted to send any items that are marked as backorders.
Sew Essential: UK based. Good range of well-priced patterns, plus a selection of notions.
BurdaStyle: Many free patterns, plus plenty of "how-tos" and oodles of inspiration. I don't use this site as much as others, as I find it quite hard to navigate, but it can occasionally come in handy. They also now sell PDF copies of selected patterns from BurdaStyle Magazine (I've never used these though as I subscribe to the magazine!)