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.
This one looks WAY more complicated than it is. I've made a quilt top with this pattern and I love it.
Zig zag quilt
Very simple basic block repeated, needs a bit of thought when it comes to use of colour and assembling the quilt top.
Single Irish Chain
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
See http://www.thatgirlthatquilt.com/2011/03/have-stitchin-weekend.html for method.
See http://patchandi.blogspot.com/2009/10/half-square-triangles.html for possible layouts
As you can see from the second link, half square triangles are a very versatile basic unit.
Improv quilt (waverunner)
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.