Hi,
I agree with the above two posts: don't alter anything in the Database.
If you're worried about looks of the ID and the numbering, use your own numbering in your front-end HTML/PHP files.
Start a counter going from 1 to the # of rows there are. This counter will be indepenedent from the mysql auto-increment and it will make your front-end look better.
Also, even if you DO change the ID #s in mysql, you're going to be putting heavy load on the database for an unnecessary reason. Think about it: if you have a thousand entries and you delete the first one, you have to change 999 entries in the table and also the many other entries in other tables you've created relations in.
Perhaps we (or just I) are not understanding your concern/question. Why do you want to "fill the gap"? if you are sorting using the ID field, then you don't have to worry. suppose you have 5 entries and you delete #3. If you add another entry, it gets an ID of 6 (NOT 3). So the order by ID still has its integrity.
-sridhar