Is there a way to password protect individual apps? Is it possible to password protect a specific Mac application?

For example, I am interested in protecting Mail because even if you cannot retrieve new emails, you still can read all the already received emails.

This is not a question about security. It's about sharing a device within a family. I don't have crucial information. I just want to avoid my girl or son to send accidentally emails from my account or prevent them to read some of them.
Regarding your comment on Paul's answer, wanting to leave your computer for a moment: you have to lock your computer. Period.

Open System Preferences, click Security (top row, second to last option), under the "General" tab, check the box for "Require password [immediately] after sleep or screen saver begins".

Then, when you go to walk away from your computer;

Ctrl ⌃+Shift ⇧+Eject ⏏

(Additional notes: Click the above line.)

Lock your Mac. Walk away. Come back, enter your password to unlock it. Secured console.