Sometimes it's hard to find what you want so I'm going to add links here to help you track things down. This is starting with UK in mind but places listed as and when I get to them.
I've also written a guide to shopping and getting make overs in store which you can read here.
BeautyMart - set up by Millie Kendell MBE (of Ruby and Millie fame) and Anna-Marie Solowij ex-beauty director of Vogue this is basically the professional edit of the best products around. So there won't be entire ranges - just the products they've tried and loved. I fantasise about what it must be like to work in their office.
Cult Beauty - as the name suggests this is the stockist of those cult products made famous by pro-artists,YouTube and Instagram phenomenons. Think NYX, Anastasia Beverly Hills, May Lindstrom and Tata Harper. If there's a US brand you UK dwellers have been wanting to try, here is a good place to check.
Daniel Sandler - available on other websites but I always like to buy direct when I can. This is the place to get the now famous, watercolour blush along with lots more incredible make-up. You can get a pro discount here to and the customer service is unbelievably good. I actually can't think of better. Watch and read tips and tricks from the man himself. If you want to try the products in person there's a list of stockists on the site.
Feel Unique - a great selection of brands, and the place to go if you want to sort of do a make-up/beauty/skincare big shop as you should be able to find most things here. If not here then Look Fanstastic (see below). I am an affiliate for this site so I may get a commission if you buy through one of their links on here - it won't cost you anymore and you can always google it yourself if you are not an affiliate link fan.
Look Fantastic - A good variety of brands, reasonable prices, quick delivery and if you look you can often find online discount vouchers. I'm an affiliate for them too (see Feel Unique above)
Louise Young Cosmetics - another brand that although available through other sites I prefer to buy direct. Louise offers a pro-discount, great customer service and amazing make-up to suit pro's and everyone else. My favourite brushes and the eye palette I can't live without are by Louise and if you haven't tried these products, you should.
Love Make-up - If Feel Unique and Look Fantastic have all the big name consumer brands then Love Make-up have the more quirky and insider ones. Shop here for Indie Lee, OCC, Niod, Ardell and Face Lace.
John Lewis - a bit of an institution with a great returns policy and reliable brands. Not quite as full-on a beauty hall as Selfridges and a great range. A pretty good place to go for an on-counter make-up. Shops in London, Norwich, Nottingham and more - you can see the full list of their stores here.
Marks and Spencer - another UK institution but one that, until recently, was not necessarily associated with beauty. Now stocking some great brands and an exclusive brand by Rosie Huntington-Whitley it's now really worth having a look around their (often badly looked after) beauty sections. You can find a list of their stores here though they really vary in size so it's worth investigating further before you visit.
UK - LONDON
Guru Make-up Emporium - a pro store that non-pro make-up lovers may want to check out and great for SFX artists. Everything from empty palettes, spatulas, fake blood, books, wig blocks and disposables to cool harder to find brands such as Delilah, OCC and RCMA. Good online shop too. High Street Kensington Tube (District and Circle lines)
Harrods - if Selfridges is all bright lights and modern, Liberty small and niche, Harrod's is like a comforting throw back to beauty hall days of yore. Great brands represented, counter-staff in suits with a ton of make-up and the sort of lighting that makes you spend money but not actually realise what your face looks like til you are out of the store. This is about the experience as much as anything else. Knightsbridge (Piccadilly Line)
Harrods Urban Retreat - a new, well, retreat, upstairs in Harrods where they have a few selected brands as well as hair, spa and make-up treatments. Carla at Hourglass does a lovely make over. Knightsbridge (Piccadilly Line)
Liberty - for more high-end brands this is a real London landmark and worth a visit just for the experience. It's a lovely place to shop with lots of little stands full of goodies - a great place for stocking fillers or beauty gifts for friends but most of the brands stocked here will do some serious damage to your bank account - Hourglass, Votary, Skin Laundry and Sisley. Oxford Circus (Central and Victoria lines)
PAM - a shop more geared towards pro make-up artists this has everything from kit supplies to fake blood. But it's great for those wanting to find products not stocked in a lot of places - Make Up For Ever, Louise Young and Ben Nye for example. The staff here are really friendly and helpful so great for those starting out who want help building their kit. Good for shopping online too. Goldhawk Road Tube (Hammersmith & City Line)
Pixi - a lovely little shop tucked off Carnaby street with gorgeous make-up and skincare products. Never had anything but great service here. Glow Tonic, Double Cleanse and Correction Concentrate are my favourites. Oxford Street (Central and Bakerloo lines) or Piccadilly Circus (Piccadilly Line)
Selfridges - their beauty hall is huge and (for some of us) quite exciting with all the top brands represented. I find you can be a bit hit or miss with the service you get here but have had great make overs with Laura Mercier (Hayley if she's there), Bobbi Brown and fairly off-hand but comprehensive help on the Charlotte Tilbury counter. MAC are nice and Tom Ford have basically ignored me. Mostly higher end brands but the beauty hall behind the main one has some more 'stocking filler' things, pop-up stands and places to get your nails done, hair styled (Hershesons) and the Cowshed Spa. Bond Street tube (Central line)
UK - NORWICH
For those who haven't been Norwich is pretty much the perfect city. Small enough to walk round with an incredible mix of big stores (John Lewis, Debenhams, Topshop etc) and little independents in The Lanes.
Jarrolds - old fashioned but up-to-date. It has a haberdashery downstairs and great make-up brands (and stationary) downstairs. Sums up Norwich perfectly.
Sephora - such a
novelty for us UK residents but probably not exciting for those of you
able to get to one whenever you want. Huge range of beauty and make-up
brands as well as their own products. I can be dropped off here and
picked up by Joe an hour or so later.
USA - NEW YORK
Ricky's - very cool and not only stocking well known brands but the go-to place for pro's too. If Ricky's don't have it - it's not worth having