After having a tooth removed, there is a gap in between your teeth, where that tooth used to be. Do you need to have a new tooth put in?
For physical health reasons, no, not at all. You will still be able to continue on with your life. Chewing efficiency will decrease but you will still be fit an healthy.
The most important reasons to replace a missing tooth are psychological and social reasons. Of course, this very much depends on yourself. Missing a front tooth that is highly visible when you smile is a strong reason to replace the missing tooth. If you live on an island by yourself (or with Wilson), then there is no social need to replace it.
Psychoglocially, you may feel that it is just not right to have a missing tooth.
How to replace a missing tooth will be covered in another post!