n your own personal computer, you're free to install whatever security software you feel necessary. You'll surely want a firewall to block hack attacks and an antivirus app to keep out malware. You may add a spam filter to protect your Inbox, or a security suite that wraps comprehensive protection in handy package. Your computer isn't accessible to random passers-by, so you may not be so worried about activity traces like browsing history.
Using a public computer at an Internet café, library, school, or even a friend's house is quite a different situation. First, you have no guaranteed that the computer is protected; it might be riddled with viruses or afflicted with a keylogger. Second, unless you're careful the next user might learn a lot more than you'd like about your online session.