Run apt-get without sudo

Open a terminal and type sudo visudo. At the end of the file (really the last line in it) type %yourusername% ALL=NOPASSWD: /usr/bin/apt-get install where %yourusername% is replaced by your username.

After that you wont be prompted for a password to use sudo apt-get install anymore but please understand this is a very risky solution, there is a reason why you need to type a password for some commands, the use of these commands without password can leave your system open for some dangers. Use with caution.

sudo is exactly made for that. By editing the sudoers file you can give users specific privileges. See the manual page of sudoers(5) for details.