The Internet tools most commonly used on workstations and servers are inherently insecure. For instance, never use the popular Telnet, POP, or FTP programs unless passwords are passed in a strongly encrypted format over the Internet. Sadly, authentication is typically in plain text, which makes life easy for hackers using packet sniffers to automatically grab scores of plain text passwords from Internet noise while they sleep. Note that any encryption between client and server requires that both ends support the encryption method. Cloaking your computer's Internet presence via a firewall is the first line of defense.
All hackers use scanning tools to quickly find weaknesses in a computer's Internet interfaces.
Firewalls work at the packet level and not only can detect scan attempts but also block them, thus making your system look unattractive or even hide its existence altogether. Be very careful about what programs you download from the Internet. Do not install software from little known sites especially. Nowadays, most download sites will include a checksum, typically PGP or MD5 encoded, which can be used to verify that the program is authentic before you install it. It's not too paranoid to make it a rule to never trust anything from the internet, as even the biggest website could be subverted by hackers and you wouldn't notice.