Airplane

I think it was my brother who taught me to fold this when i was a child. Simple and easy to fold.
airplane:folding instructions

Sunburst (small)

This is done from a single origami paper. Each half rectangle gives a sunburst. The earlier sunburst posted was done with an A4 size paper. It is easier to practice the design with an A4 size paper first.
sunburst:folding instructions

Basket

This has a practical use too. Yes, you can actually carry small items in it. The handles are stapled so that they do not slip out.

Boat

I learnt to fold this as a child. It is a very simple design and a good start to introduce a child to paper folding. If folded with a sturdy paper, it should float on water.
boat:folding instructions

Iris

The petals can be curled more with a pencil. This is also called a lily in some books. Make a bunch of them to have a beautiful bouquet.
iris:folding instructions

Crane

One of the first designs that I learnt to fold was this traditional japanese crane. Can be hung on a string.
crane:folding instructions

Source:Origami for Everyone

Ball

I have always called this cube a ball. It is also called a waterbomb. Can be deflated.
ball:folding instructions

Source:Origami for Everyone

Goldfish

Sunburst

Made from a rectangle paper(2:1). Can be folded away. Hung on a string.
sunburst:folding instructions

Flowerball

Made from six flowers, the corner flaps of each flower are glued together to make this ball.It is a decorative item. Closer view

Swan

An easy to fold design. You can have a whole family of swans by making smaller versions of this design.

Dog

This a very simple design. Not much fine details so it is rather easy to fold. Compare with howling dog.

Source:Origami& Papercraft; Jackson, Paul; Anness Publishing Limited 1999

Poinsettia

This is a very interesting design. You can hang it as an ornament or place it atop some other design. Smaller versions of this can be added to make greeting cards. Nice to have for the christmas season.
poinsettia: folding instrutions

Heart

This is a very simple design with minimal folds.
heart:folding instructions