For piecing, it depends on what I'm working on. If I'm doing something where I need to be super accurate with seams and matching points, then I use aurifil 50 (2ply). If I'm working on a crumb quilt, string pieceing or doing improvisational piecing, then I might use Coats and Clark dual duty, aurifil, any of a number of vintage threads I've gotten from yard sales, eBay or estate sales-- just depends.
For quilting--again, it depends. If I'm working on a quilt that is to be used I will generally go with something like Isacord since it's good and strong and I know it will hold up through washing, etc. For art pieces, I use whatever thread will give me the effect I want--if I want the quilting to only show as a texture or for SID I might use something like wonderfil/invisafil (100wt) since they won't show at all. I've used silk, embroidery poly's, cotton, etc. in different weights depending on how much sheen I wanted, or for textural differences.
Rob