Very sturdy; I've had them for years and never had a problem. The only thing I would recommend is that if you stack these 3 units high (as I've done) that you attach the top to the wall with some sort of a bracket.
Because you can attach the top middle and bottom shelves wherever you want relative to the sides, you can break up the pattern and do stylish things, i.e. create as smaller space between sections of records where you display chachkas or whatever.
Also, be sure the one you're getting has the holes and pegs for stacking (I'm assuming there are variations of this model out there). I got mine at Home Depot and they cost around $13 or $14 a throw at the time.