list ranking

We have a set of records in a table that needs to be ranked. We thought of adding a ranking field, but the problem is that the ranking could change often and there could be additions and deletions from the list. Updating this ranking field is quickly going to get messy.

Is anyone familiar with link surgery? Can we do this with a doubly linked list? Is there a standard database solution for doubly linked lists? or another way to solve this that I don't see?
Any suggestions on structure would be greatly appreciated.

Thanks
Jodi