At a new mums support group we were advised to try the 10-minute test with things you personally would normally iron. Fold or hang straight after drying, BUT don't expect it to look perfect at that stage. When you wear the item, check in a mirror after 10 minutes. Depending on the fabric, your body heat may make any remaining creases drop out. If you don't think it looks noticeably different from usual after the 10-minute test, do you need to iron it in future?
Washer - dryers can't usually dry a full load of washing effectively, so maybe try removing some of the load after washing, hang that on a rack, and see if you get better results from tumble drying a smaller load.
Sheets depend on the fabric. Fine weave pure cotton doesn't crease much - or the creases in a fitted sheet drop out quickly. However, coarse-weave cotton seems to crease much more.
School uniforms - the M&S trousers we use have a permanent crease and ironing damages it. I take them straight out of the dryer and line the creases up carefully then hang on a trouser hanger. Works brilliantly. I did try ironing a pair to check. Couldn't tell the difference, except that I had partly knackered the permanent crease by ironing over it 
School shirts are non-iron. They don't look perfect when hung straight out of the dryer, but as per the 10-minute test, residual crinkles drop out quickly. Where a jumper is being worn over the top, I've not been able to see any difference from the small bit visible at the neck!
I expect most people know the trick of hanging things in a steamy room eg bathroom, to help wrinkles drop out. Most useful for suits but also spruces up other things.
Lots of people find ironing therapeutic. I'm not one of them, but it strikes me as a relaxing way to bring a small piece of perfection into the world. Probably a metaphor for fighting to keep order in a chaotic world 
If you find it enjoyable then it has value all of its own, like crafting.