The most familiar pattern to people is the "six way weave". It has two vertical strands, two horizontal strands and two diagonals. It is a pretty, practical weave that is not too difficult to do.
Then there are loads of closely woven patterns. These take a lot of patience and much longer to do, but are quite beautiful.
There are also basket woven seats using round "centre cane", this kind of weaving is popular on a lot of conservatory furniture. There's willow and cane seating too and all sorts of other combinations of materials.
Then there are all of the fans and medallions of all shapes and sizes
There are so many patterns! If you want to buy some cane, or would like to know more, then please visit Seat Weaving Supplies.