I wrote this out for a friend who I'm gonna help get started with patchwork and I thought it was worth sharing for anyone else who might be looking for good beginner patterns. I didn't bother with strip quilts or quilts just made of regular squares etc.
Comes together v easily. Fabric choice is important. I'm halfway through making one at the moment.
String quilt. http://www.filminthefridge.com/2009/04/24/a-colorful-string-quilt/
This one looks WAY more complicated than it is. I've made a quilt top with this pattern and I love it.
Zig zag quilthttp://beesquarefabrics.blogspot.com/2009/03/how-to-make-zig-zag-quilt-without.html
Very simple basic block repeated, needs a bit of thought when it comes to use of colour and assembling the quilt top.
Single Irish Chainhttp://www.purlbee.com/sherbert-irish-chain-quilt/
Simple, traditional and effective. I made one for my sister two years ago (see pic). Lots of patterns are based on this block design.
Half square triangles
for possible layouts
As you can see from the second link, half square triangles are a very versatile basic unit.
Improv quilt (waverunner)http://waverunnerquiltalong.blogspot.com/
This quilt can be v simple and effective and quite creative to make. Fabric choice is v important and you need to be fairly confident about making design choices.
Another classic. A bit more time consuming to piece. This one comes alive depending on how you use colour and how you arrange the finished blocks.
This is the first proper quilt I made. The instructions online are very clear and thorough and helpful.