First of all, in the spirit of full disclosure, I really don't iron much. Really not at all.
In fact I can't remember the last time I ironed an actual article of clothing. My husband irons his own shirts when absolutely necessary. Don't be too jealous. He doesn't cook. At all.
I have, however, ironed quite a few curtains in the last few years.
That said, this is how I avoid ironing clothes:
First of all, hang things up while they are still damp. I only dry shirts and pants in the dryer for about 10 minutes (this also helps so they don't shrink too). Then I hang them up on hangers and smooth out the wrinkles. (Also saving money on your energy bills. Yay!)
If something you pull out of your closet to wear is still a little wrinkled, take a squirt bottle with water in it and squirt the item lightly then smooth out the fabric. This actually works really well while you are wearing the shirt, skirt, etc. (Unless it is wet and you sit down and press more wrinkles into it while it is damp.) I will usually squirt down something I am wearing and then stay standing to do my hair or makeup while the article of clothing dries completely.
I learned this tip from one of my college roommates the day I went to a Catholic worship service with a guy I worked with. It was an interesting experience. (The worship service was interesting, the guy was "interesting".) I borrowed a dress from her and it was wrinkled so I said I'd wear something else. She had me just squirt it off and I couldn't believe how well it worked.
This is especially good to do in the summer (kind of like the swamp cooler effect).
We also take a little squirt bottle of water with us when we go to the fair, the zoo, etc., any place where you get really hot. You can just squirt down your little kids and they will stay cooler. (Um, obviously if you are wearing a white shirt you might want to only squirt the water down the back of your shirt.) Also make sure to squirt it only on your clothes if you are wearing sunscreen so you don't wash the sunscreen off of your skin.
That's it for now. I'm off to get a load out of the dryer.