Does it eliminate or reduce the chances of getting a virus? malware? adware? spyware? It says that it keeps you from getting cookies and temporary internet files. If I go to a porn site using that method, will I be less likely to get unwanted software on my computer? Will I be less likely to get spam? I’m asking for a friend of mine. 
No.
It prevents those things from being saved after you close the window. You still need them for the sites to work.
Not really.
No, but nobody’s going to send you spam unless they somehow acquire your email address.
I’m answering on behalf of Grover Cleveland.
ETA: Using a system like AdBlock Plus will do a lot more for blocking malware than using private mode.
friedo answered the specific questions, but in short–private/incognito mode is mostly to prevent other people from getting on your computer and seeing what you’ve been up to. It has nothing to do with protecting against malicious sites or safeguarding your identity.
Its much easier to run ccleanerafter exiting your browser. (download the free version)
I have mine set to clean each time windows reboots. It clears cookies, temp files, browser history, and empties the recycle bin.
Use Firefox in private browsing mode with the AdblockPlus and NoScript extensions. Together those extensions block tracking cookies and scripts, plus prevent common browser hijacks. Even better, browse on a machine (real or virtual) that you do not keep sensitive data on or log into important accounts from. That limits the damage that can be caused to you if your first-line defenses fail.
Of course, the best defense is not to visit sites that will try to do bad things to your computer.
Plus, keep your computer up to date (windows updates) and run an antivirus program.
No computer is 100% secure, but from what I’ve read, a lot of the common exploits found are for older security holes. being current with your updates and AV will plug a lot of common holes.
AVG (free) is a handy antivirus. The trick is to navigate the menus carefully when downloading it to not accidentally end up with a trial of the paid version instead.
Another handy trick if you are a bit tech-savvy is to create a non-privileged userid to do some types of browsing. If the process doing the downloading is entitled to install programs on the PC (Administrator or power user) then the exploit is that much farther ahead to taking over your computer. (Of course, don’t use XP. I’ve been told that there is a bug in XP, which MS has declined to fix, that any logged on user can elevate itself to administrator status.)
If you’re anal and love to fiddle, turn on the firewall service on the PC. It should alert you if odd processes are trying to get out on odd ports.
The only thing it will protect you from (the only thing it’s meant to protect you from) is other people using your computer finding out what sites you’ve been surfing to, or getting your passwords from them.
(Firefox, at least, explicitly states as much, though you need to go to the ‘read more’ link to get the mention of malware.)
Oh, one more layer of defense everyone should employ: different passwords for different accounts. That way, if a site is hacked or you’re keylogged* on one account, the badguys only have access to that one account.
*Which is why you should do your online banking on a separate machine from your general web browsing.
Private mode does prevent some types of tracking between sessions. But not within a session. It’s only a small part of hygienic web surfing.
Check out a program called Sandboxie. It runs your browser in a protected ‘sandbox’ environment which is erased when the browser exits. Any change the browser makes to the registry, any files downloaded, any cookies saved, etc. are written to a temporary location and deleted when the browser exits. If you happen to download a virus, it only lives as long as the browser is running. If it tries to modify your system, the change only happens in the sandbox and will be deleted later.
A virtual sandbox environment will do a much better job of protecting your system from attacks than running in private mode. Private mode is just more of a convenient way of deleting your browser history.
The disadvantage of running your browser in the virtual environment is that any settings you want to save will also be lost. This might be things like browser updates, Flash updates, saved passwords, history you want to save, etc. To make permanent changes in your browser, you’ll need to start up the browser outside the sandbox and make those changes. Then the next time you start up the sandboxed browser, it will reflect those changes.
Does Sandboxie prevent you from executing downloads you actually want?
You can execute them from the sandbox, but then they live in the sandbox. Any files they update or changes they make will be removed when the browser closes. Also, the program itself will be deleted since it’s also in the sandbox. However, Sandboxie recognizes when something is written to the browser’s download directory and it will ask you if you want to move the file to the same location out of the sandbox. If you say you want the file moved, then sandboxie will copy it to the corresponding directory on the real system and you can run it from there as a normal program.
Another vote for Sandboxie. Takes a little getting used to, but it’s a much safer way to browse. Just set your browser up how you want it outside Sandboxie, then when you actually browse, always use Sandboxie. Each time you start your sandboxed browser it will revert back to the previous state, no changes the browser makes while sandboxed are saved to your actual hard drive directory structure. But the browser, extensions, and malware think they have the full run of your hard drive and will run normally.