Honestly the safest and probably best way to do this for the long or short term is leatherback's original suggestion.
Changing ID's like that is bad, it sort of goes against a lot of the rules that make DB's so efficient.
The best situation, as leatherback suggested, is to create a new SortOrder column. You can then even use js or ajax to move this around and save. The user would be none-the-wiser, and your system will be more stable than what you were originally asking.
For mysql it is as simple as
alter table simple_table add column SortOrder tinyint(1) not null default 0;
or some other value other than tinyint, if you are sorting many different records.
I strongly suggest not moving around ID=>value pairs.