We've actually done both.

Keisha's was such a sudden death we never really had any time to think of what to do for her. When she died at the vets I had them put her in the back seat of my car and I drove her home. We burried her in her favorite place in the back yard (where she used to lay on my flowers). I hated the thought of burrying her, but at the time it was the only thing we thought of.
Now I feel we can't move because I don't know if I could bear the thought of leaving her.

With Angus we were prepared. I had bought an urn and a necklace for some of his ashes so I'd always have him with me. The only time I don't have him around my neck is when I take a shower. And his urn stays in our bedroom, where he spent most of his last days. There are also other momentos with it.
I didn't like the idea of having him cremated and it bothered me for quite a while after we got his ashes back. But now I wouldn't have it any other way.