What is the best cut of beef to use for stews?
Assuming a long, cooked stew. I cut up a well marbled chuck steak usually and chuck is what I'd recommend.  You want enough fat that as the stew cooks long, the fat will render and leave nice, tender meat.  Too lean and you're left with boiled shoe leather.

If you want a quicker stew, use a leaner cut of meat like sirloin.  It will have a lot of flavor but you shouldn't cook it long at all.  A fatty cut in a short stew will end up very fatty and often tough (with a cheaper cut like chuck).