Turiba is by far the cheapest hostel in Riga, at least for double rooms. The double room we got was 13 LAT per night, which equals about 20 Euros for 2 people.
Turiba hostel is part of the Turiba business school, so you live in the sleeping house of the students. this is not a problem, they are all very friendly, helpful and speak english well.
the hostel is quite an ugly "block" as known from the soviet times... it's also not lying in a beautiful part of the city, but thats not the biggest problem as described below.
The room was clean and not too small (in fact we got a room with 4 beds as "double room"). there was a large cupboard and small bed boards.

Another reason why it's so cheap might be that it's a little outside the city center. all the "normal" youth hostels for tourists are directly in the center. but this distance is not a real problem, as there are different possibilities to reach the center easily

1) train... more