An urn or box can be anything that you want it to be really. It all depends on what you want.
I suggest checking out Etsy - lots of people on there make ceramic urns that are very nice, there are also quite a few wooden ones.
There are also a few places that will make jewelry that you can place some of the ashes in, or have stones made from the ashes. Some will create a piece of artwork with the ashes incorporated into it. One of my old friend's mother died, he had some of her ashes mixed into tattoo ink and had a memorial tattoo done. I don't know how sanitary that is, but it's beautiful and he never got an infection or anything from it.
Here are some of the urns on Etsy -
http://www.etsy.com/search/handmade?...ery&ship_to=US
Here's a place that does artwork and glass pieces from ashes -
http://www.artinashes.com/Cremation-Art-information.php
And some jewelry where you can incorporate ashes -
http://www.ashestoashes.com/
The urns that we've received from the vet all depends on where you get it done. Our dog had to be put down at the emergency vet - they let us choose if we wanted a ceramic urn or a wooden box. We chose the box and it's a lovely little one. The vet where we had one of our old cats cremated at didn't given an option and we got her back in a really odd looking ceramic urn that had little flecks of colour through it - I hate that urn.