You shouldn't have a plug coming directly from your cable or DSL device (sometimes incorrectly called a cable or DSL modem) into your computer. That network plug in your computer was designed to be connected to a TRUSTED network, not the Internet.
The cheapest and easiest solution for this is a router. Typically, people use routers to share an Internet connection with multiple computers in a household, but even if you only have one computer this is a good investment. The router, unless it's default configuration has been radically altered, will not allow unknown entities on the Internet to connect to your computer. In fact, without using ultra-sophisticated network-cracking techniques, unknown entities on the Internet will not even be able to tell your computer is there.
The router itself cannot be attacked because it doesn't do anything but route information for other computers. Unknown entities can see the router, they can try to attack it, but they can't get it to do anything, so the attacks fail to cause any harm.
Right out of the box a router will greatly improve your security. To increase your security a bit more, take time to change the default password for the device. Write it down on a label and stick the label to the bottom of the device (If anyone malicious can get to this label, they don't need the password).
Linux hacker? Running a server? ESR tells all here.
It almost seems too obvious to say, but there is no more secure computer than one that is off. Your Internet connection may be full time, but there's no reason to keep your computer on full time. Turn it off. You save the electricity bill, the Grid saves the power, you computer's moving parts (disk drives) save wear and tear.
There used to be a school of thought that maintained that leaving a computer on extended it's life. The reasoning was that provision of a stable thermal environment (i.e, a constant internal temperature) was protective of the components. The theory went that frequent cycling of power would repeatedly warp the circuit boards and cause them to fail over time. These theories were popular among those with Cindy Crawford screensavers.
Your computer will become obsolete long before thermal cycling causes any noticable wear. Save the money, save the grid, save the environment, turn it off when you're not using it.
I am not a fan of Microsoft, but we can have that conversation later. I do buy licenses for my Windows computers, however, even though I'd rather almost any other company had the money. Why? Because it's risky to use a Windows computer on the Internet without applying the latest security patches. This is not because of some clever marketing ploy by Microsoft (not at this writing, anyway), it's because the default installations of Windows are riddled with well-known security problems. There are still enough of these machines on the Internet to make exploitation of them interesting, so it's still going on and probably always will be.
Windows is an easy target for computer vandals and there are many angry & malicious programmmers who live to embarrass Microsoft as much as possible. Microsoft patches most of the holes eventually and fortunately they now consider it important to their marketing strategy to make these patches available and easy to apply. Later versions of Windows can be made to do this almost automatically.
Take the time. Do it. Pay the piper. Like a NYC parking ticket, the cheapest way out is to pay up. If you are using an older version of Windows that is no longer supported for security updates (Win 3.1, Win 95, Win 98), upgrade or don't use that computer on the Internet.
I like this one, but any of the major players will do. This is particularly important if you also use Outlook Express and/or Internet Explorer (see next precaution) on a Windows machine, but having virus protection is important enough to do even if you take all the other precautions.
Not only do you need anti-virus software, but you also need a subscription to the update service for that program. Anti-virus programs work by comparing the patterns in the information on (and arriving at) your computer with the patterns found in malicious programs. Since there are new virus programs being released regularly, the patterns used for matching need to be updated also.
Security is always a trade-off between safety and convenience. Safe things (locks) are inconvenient. Convenient things (doors) are unsafe. Microsoft has long made convenience a central characteristic of their products. Along these lines, they have pursued a strategy of making Microsoft products the most convenient to use with their operating systems--click on a icon in one Microsoft program and it will open up another Microsoft program and do something automagically. Like an open door, it's convenient, but it's not safe.
The biggest problem is e-mail. E-mail can deliver a virus/trojan program right to your computer that can destroy your computer (or do any number of nasty things) with a single click if your e-mail program is able to automatically do a bunch of other things. For this reason, it is a bad idea to use Outlook Express with Windows. Similarly, if you read your email with a web browser instead of retrieving it to your machine (yahoo, hotmail, etc), using Internet Explorer to do that is a bad idea. Why do you lock your doors at home and in your car? Because the convenience of unlocked doors is not worth the risk of burgulary. The same rule apples here.
Any other email program is safer than Outlook Express, and the simpler it is the better. I recommend the use of Thunderbird these days.
In the same vein, if your web browser (what you are using to read this) can accomplish a number of other things on your computer, perhaps that is because it is made by the same company that made your operating system. It's very convenient to use, isn't it? You can use it to look at any file on your computer, and clicking on those files will make them run. That's very convenient. Your convenient browser will also install software automatiically, change your computer's settings easily, and do most anything you can think of on your computer. Yep, that's convenient.
A browser should be used for reading web pages and not much else. I use FireFox regardless of what operating system I am using. It's a better web broswer than Internet Explorer. It has a number of features that are useful: tabbed browsing (you can have multiple pages open in a single window), pop-up blocking, on-demand cookie management (you can choose to accept which cookies) are just a few. There are other choices as well, any of these is safer than using Internet Explorer