Since you say it has a cardboard back I'm guessing you have prefab shelving?
In my experience, it's kind of difficult to make it to where they are not at least a little wobbly. But it just sounds like they need all the fasteners tightened.
If your actually wanting to make them more sturdy than that, I dot think little L brackets are gonna help you much. I would measure how wide each shelf is then go to the lumber yard and have some 1x4s cut to length, center it on the back of your shelving and screw it in. They should be pretty sturdy then.
If your wanting something better, it would then be time to learn woodworking and start making your own shelves. Plus it can honestly be cheaper than buying prefab also.
Edit:
Forgot to add tools...
For everything I mentioned, you would need:
Philips/flathead screwdriver to tighten up loose fittings.
A drill with a small bit and screws to make some pilot holes if you take the board option.
I don't think it is them being loose, they were always wobbly.
I'll get some brackets soon. I still have some shelf space, and I can;t see my collection growing that big any time soon, but I would like to compress it.
I have some woodworking skills, I was a set builder when I was in my High Schools drama club, I just to not have access to the tools I need, or the time to build it, I start collage in 2 weeks.
I was thinking of going to Home Depot or something and getting the wood cut there. and assemble it at home.
For making adjustable shelfs, would this work for the sides
http://www.modernvictorygarden.com/photos/HIdden%20Album/Jan%2016%202010%20005.jpgOr would I have to drill holes manually?