I would try an Acrylic/Polyester blend yarn if you haven't liked any of the strictly Acrylic yarns. Also, have you only got Red Heart SuperSaver? Because they do make a lot of other kinds of yarns that many people find to be more pleasing. The same with Lion and Caron. I bet you've tried Caron Simply Soft and didn't like it much, eh? If you haven't though, give it a try. It is a worsted weight, but feels a bit meatier than most yarns of the same weight.
There are lots of yarns made from other materials, but the "stranger" they are, the higher in price they tend to be. However, if you're only making small things then you could easily indulge in a hank or two of things like bamboo (If you want to see bamboo yarn in action, there is a basket on knitty's website here) Cotton yarn is pretty danged cheap, though, and shouldn't give you any troubles. There's linen yarn, which when knitted makes a rather stiff fabric but the more you use it and wash it, the softer it becomes - Much like old linen towels. There are even soy-based yarns! I'm sure there are people on here with more info on alternative fibers.
Also, remember that you can knit with ANYTHING! Right now I'm cutting up old t-shirts and jeans to knit into panels for a rug. They're 100% cotton, and it's really fun! I've also seen people make things out of old plastic bags. If you want to find out how to make yarn out of THAT, I've got another link - Just PM me or post here if you want to see it.