I don't pin much, when I'm piecing a quilt, but I NEVER put on borders without measuring and pinning. This makes a huge difference in whether you have a square quilt or not.
This blog post on Jenny's Doodling Needle about Let's Talk Quilt Borders says it really well, and has some pictorial evidence about why border application is so important.
Carole at From My Carolina Home has also done a great tutorial on why it is important to measure and pin borders properly to have a flat, square quilt, and to keep those borders from being too friendly (aka wavy).
I do an anecdote from one of my quilting friends...her first quilt she measured across the quilt in 3 places, found an average length, measured and pinned her borders, and had a square quilt. As she was working on her 2nd quilt, I noticed her sewing on the borders and then trimming them to length. I made some comment about measuring and pinning (I hope I wasn't being too bossy), but she said I made one that way and now I'm making one this way....
After she had quilted that 2nd quilt, she said she would be measuring and pinning from now on.
It is time consuming, and sometimes a hassle, especially with really large quilts that are hard to layout and measure, but worth it in the end.
So, please, please measure and pin your borders.