I used to fold a lot of origami when I was littler. Don't remember as many anymore, but once in a while I try to relearn a few. Below are some bookmarks I keep of some nice ones to remember (or reference if you don't remember). Usually I care only for those that require no cutting or additional accessories (just the paper and folding). Kind of defeats the purpose otherwise - at least to me.
If you know any other nice tutorials, do add. I'm always wanting to learn more - and perhaps figure out a few that I used to know how to make but forgot lately.
<div class="list">
Materials:
Best Origami Paper Stores Online</div>
<!--ADS-->
<h3>Looks Only, Non-Locomotive</h3>
<div class="list">
Butterfly - Diagram uses a square, but it doesn't explicitly say a square sheet is required.
Heart 1 - Plain, no fancy folds on top. Square paper.
Heart 2 - Appears split in middle. Requires square paper.
Lily Flower w/ sepals - Has a bit of a squarish 3D shape to it but the sepals add a nice touch, requires square paper.
Nuclear Crane - Three-headed and three-tailed crane.
</div>
<h3>Boats</h3>
<div class="list">
Sailboat - Boat with a sail, not as wide a base though.
Sampan Boat - First boat I learned to fold... can't believe I forgot how to fold it though and had to look it up. -_-
</div>