I rarely do it, because, well, you really don't get any brownie points for doing it. The exception is around Christmastime.. I've noticed that they'll sometimes offer a $1 coupon towards a future purchase if you select standard over two day, and that might be a good time to take them up on that for non-rush items.
You know how Amazon orders "guaranteed delivery dates" for certain items, like new release movies? The guarantee isn't that if you don't get your movie on the date, the movie is free, it's that they're refund the shipping. Well, as a Prime member, when something misses it's guarateed date (which does happen to me occasionally), you don't get a refund on the shipping or any sort of credit, because the shipping is considered "free". I'm not sure that's directly relevant to your question, only that they don't do anything to make it up to Prime members when they miss a "guaranteed" date, so I'm not feeling an overwhelming incentive to try to help them out either. They also have a whole new class of items they call "add ons" where even though you've got unlimited Prime shipping, they will not send those items out unless you've already spent $25 on unrelated items in the same transaction, which I think makes the Prime thing a little misleading now.
Amazon has done more right than wrong by me, and that's why I'm still a customer, but I'm not feeling any incentive to go out of my way for them in the way I might for a local independently owned shop or family business.