Securing Your Computer
If you want to trade securely, you must observe some security precautions. Along with the concerns of conventional online banking, trading with Bitcoins also requires physically securing your computer.
Operating System
Even the best operating system is only as good as it is maintained and configured.
Updates
In general, make sure to install all the safety-related updates from the manufacturer. Modern operating systems have an automatic update feature that is essential to activate. This ensures that available updates are always installed as soon as possible. This is important because as soon as the manufacturer patches a security issue, the error usually is already well known in certain circles long before the patch is released.
Virus Protection
To minimize the possibility of malicious software like viruses or trojans finding a home in your computer, it is important to install a functioning and current virus scanner.
Also it is important to realize the principle of "more is better" does not apply. Installing two, or even more, virus scanners on a computer can greatly reduce system stability, speed, and usability. For home users, there is a variety of virus scanners that are free for home use that are completely sufficient.
For more detailed information please visit the corresponding Wikipedia article.
Firewall
A firewall protects against outside access to your computer and installed applications, preventing unauthorized access to the network. Since no virus scanner can detect all potential pests, a firewall is therefore a useful protection against trojans, for if one does happen to get installed, it will be unable to transmit passwords or similar information.
If you do not have a well-configured hardware firewall, or do not know if you are behind one, it is absolutely necessary to install and configure a software firewall (one typically comes built-in to the operating system). A software firewall is a useful addition to a hardware firewall, since there is a possibility that another computer within your network is already infected, or has some other nefarious intention.
Also, a firewall is only as good as it is configured. The rule "the stricter the better" definitely applies. It should only allow applications that you know and trust to access the network. Some firewalls will recognize the ports used by particular applications to communicate with the outside world. If this is not the case, you should consult your firewall's documentation for direction on how to open a port. The port that Bitcoin uses is port 8333.
For more detailed information, please visit the corresponding Wikipedia article.
Theft
To ensure secure trading, the physical components of your computer, as well as any media (USB stick, external hard drive, etc) on which your wallet is stored, must be secured.
Anti-theft
Many laptops and even some desktop computers can be secured with a cable designed to prevent theft. Such cables are named after the largest manufacturer of security cables, Kensington, and are designed to connect to the computer's "Kensington Security Slot". Use of such a security cable allows a computer to be "chained" to an immovable object such as a heating pipe, or a specially mounted bracket. This will not make theft impossible, but makes theft incredibly difficult without the proper set of tools.
Encryption
Since computers can not always be chained up everywhere, and even the best security cable is not immune to bolt cutters, it is important that the medium on which you store your wallet be encrypted. See here a list of available encryption software.
Although the computer might have been stolen, at least the thief does not have access to your wallet and cannot send Bitcoins in your name. Despite being encrypted and safe from prying eyes, your wallet is still irretrievably lost, which makes it important to regularly keep a backup of your wallet.
With processors always getting faster, brute force attacks on passwords are getting easier and easier. To stem this advance in password-breaking, a good-length (>12 characters), complex password with special characters should be used.
Users need to be informed, understand, and be up-to-date with the concepts behind password cracking in order to know the nature of the password they should choose. This Ars Technica article is very informative about this. In some cases and some algorithms, an extremely long random password with many types of random characters is required. Even passwords like these aren't immune.