Tango sneakers and tango practice shoes
A good pair of practice shoes can really save your feet.
They're not necessarily just for practice, either – quite often girls change into their tango sneakers towards the end of an especially long milonga, and some girls will do a whole milonga in practice shoes.
NeoTango
Neotango have a website and do do mail order, but as far as I can see they only have one pair of tango sneakers shown on the website. They do a fairly wide range, though, in lots of different colours. They offer leather, suede (cromo) or half-suede (half-cromo) soles, and there are US and European suppliers. Update: there is now also a non-flash website for European customers, with prices in Euros.
Tango Brujo
Tango Brujo was only founded a few years ago, but their shoes have already got a devoted following. They have a reputation for being super comfortable, and are popular with a lot of nuevo dancers. Tango Brujo itself is a dance school, but has a shoe and clothes store on the ground floor. The owners of the school wear Tango Brujo shoes, which is a good sign. It has a website which has finally started selling shoes (though it's often offline, in which case you only see a splash page). There are also some US and European suppliers, and there will be more as they become better known. They do practice shoes and tango sneakers for both men and women.
Fabios tango sneakers
Fabio's only do tango sneakers. Their big selling point is that they will make you a pair to your specifications, letting you choose from a range of designs, colors and materials, so you can get something very individual. Some people adore them. Others really don't. I know a couple of people who feel they're kind of flimsy. I personally found them very soft, supple and comfy, but not very supportive. Their basic sneaker style can be worn by either men or women, and they also do a women's range which have either a higher (2") rubber heel, or a full stiletto heel (which I've never seen anyone wear). The soles are suede, and for me this is their big advantage over mainstream brand dance sneakers, which I always find have too sticky a sole.
Darcos Tango Shoes
Another fairly big name. They have a big shop in Buenos Aires which sells music as well as tango dancewear and tango shoes, and other dance shoes. They claim to be 'magic shoes', and are more generous with their padding in the soles than most other tango shoe brands. They do tango sneakers and tango practice shoes in some of the craziest styles I've ever seen.
2×4 al Pie
I'm not sure I can really class these as tango sneakers, but I can class them as practice shoes. They don't do any heels for women, only flat leather shoes. 2×4 have a unique selling point – they have interchangeable soles, so you can swap between suede, leather and rubber soles. They're best known for their men's tango shoes, and several of the really big names wear them. They have a distinctive 40s look.
Regular dance sneakers
Some tango dancers like to practice in mainstream dance sneakers – you know, ordinary dance shoe brands, the kind that are designed for street dancers. I personally have never found a pair I liked – most of them are very chunky and hard, and I find it very hard to pivot in them. Personal taste. I've been happier getting regular sneakers and gluing suede to the bottom! Works surprisingly well.