In some places, one can find 2 € watches that work well for one week, then they die. Normally, a quality replacement battery costs more than 2 € in the EU.
But there is a category of pretty nice watches — cheap Chinaware — in the price range of $10…$25 that seem to work quite well! (Those Chinese are going to ruin us all.)
The above watch is a military-style Overfly watch by EYKI, available in several colors. On DealExtreme, with free shipping from China (so you’ll have to pay custom duties and VAT), they’re $15.50 — black / dark blue / green / sand (OK, I couldn’t find the green one there, but on the other hand there are several other — cheaper! — watches, even from the EYKI Overfly range, such as this one or this one). On eBay, for less than $25, there are several offers, even with shipping from within the EU, from Frankfurt: black / green / black / sand / black / dark blue / black / green; also from Hong-Kong: all colors / all colors.
There is a review of these watches on a forum, with real-life (not marketing) pictures, which seem to prove a rather good build quality: take this, this, and this. There is also a silver version, and the movement is by Seiko Epson, apparently.
There are many other models by EYKI, such as this Flywheels inspired by Hamilton watches — but no day of the week in this case:
Oh, those Chinese people…