I nearly always use double-fold bias binding on my quilts. The fabric is cut at a 45 degree angle to the selvages. The strips are sewn together, then folded in half length-wise to create two layers of fabric before sewing along the quilt edge. Bias binding stretches a little so it is a must on any curved edge. The downside is that some quilters find bias binding tends to pull out of shape on straight edges and may even stretch the edge of quilt, creating ripples. In theory, double-fold bias binding is the most durable type of binding because the fibers in the binding are not aligned with the edge of the quilt. A straight binding cut exactly on grain will have one thread running right along the edge of the quilt and this thread will get a lot of wear and stress, so the binding could eventually split right along this thread. However, the reality is that straight grain binding is rarely exactly on grain and will be even more "off" after sewing, so it is not likely that one single fiber will run along the edge.
So double-fold, straight grain binding works well on straight edges. It was the perfect choice for Keep Calm and Sew On, where I wanted the stripes to be straight, not bias, plus wear along the edge is not a big issue for a wall hanging.
I have a few books I frequently refer to for bindings and other edge treatments. A Fine Finish, by Cody Mazuran, is an excellent resource for how to do anything above and beyond the most basic binding. This book is out-of-print but used copies are available on Amazon.com. It covers putting binding on a curved edge (like a double wedding ring quilt), using piping along the edge with and without binding, and other decorative treatments. It is a worthwhile addition to your quilting library.
Borders, Bindings, & Edges, by Sally Collins, is another good resource. While this book covers binding techniques, it includes unusual border treatments, especially pieced borders.
Darlene Zimmerman's book, The Quilter's Edge, is another good resource for borders, bindings, and finishing techniques. If you've been wondering how to do prairie points on a quilt, you will find out how in this book.
Well, I have lots of binding to attend to. Better get cracking!