Here's some information about common files that you can download from the internet, and a little bit about using these files for their intended purposes.

Compression Files

.rar .zip .ace .r01 .001 

These extensions are quite common and mean that your files) are compressed into an "archive". This is just a way of making the files more compact and easier to download.

To open any of those archives listed above you can use WinRAR (Make sure you have the latest version) or PowerArchiver.

If those programs aren't working for you and you have a .zip file you can try WinZip, or 7-zip.

If the two first mentioned programs aren't working for you and you have a .ace or .001 file you can try Winace (Trial version).

.cbr .cbz 

These are usually comic books in an archive format. a .cbr file is actually the same thing as a .rar file and a .cbz file is the same as a .zip file. However, often when opening them with WinRAR or WinZip it will disorder your pages. To display these archives properly it's often best to use CDisplay.

Multimedia Files

Video

.avi .mpg .mpeg .divx .xvid .wmv .asf

These files are usually movies or TV shows, or a host of other types of media. They can be viewed using various media players including Windows Media Player, but I suggest using Zoomplayer, BSPlayer, VLC media player or Media Player Classic. Also, you'll need to make sure you have the right codec's to play each individual file. Codec's are a tricky business sometimes so to help you out with your file and what exact codec's it needs try using GSpot. It tells you what codec's you need. Then just look on the net to find them.

The K-Lite Codec Pack is a collection of codec's and related tools. Codec's are needed for encoding and decoding (playing) audio and video. The user-friendly installation is fully customizable, which means that you can install only those components that you want.
There are three versions of the K-Lite Codec Pack: The Basic version, who fits on a single floppy disk, contains only the most essential codec's and related tools. The Standard version contains everything what is needed to play all the commonly used formats. The Full version contains even more codec's and also has encoding support.

K-Lite Codec Pack 2.27 Full (8.14 Mb)
K-Lite Codec Pack 2.27 Standard (4.35 Mb)
K-Lite Codec Pack 2.27 Basic (1.33 Mb)

Alternately you could download codec's individually, here's a few.

ffdshow (Recommended! (plays many formats: XviD, DivX, 3ivX, mpeg-4))
XviD codec
DivX codec
ac3filter (for AC3 soundtracks, aka "5.1")
Ogg media codec (for .OGM files)

Can't find what you're looking for? Check out these sites...

DivX-Digest
Digital-Digest
Doom9
VideoHelp

.mov 

These are QuickTime files. There are alternatives to the original program, if like me, you don't like it. Check out QuickTime Alternative or Media Player Classic which can play these files so long as you have the codec already installed.

.ra .rm .ram

These are RealPlayer files. I'm not a big fan of Real player. It installs lord knows what on your system and never really goes away when you want to uninstall it. Still if you insists you can get the player here. There are however alternatives to the original program, check out Real Alternative and Media Player Classic

vcd/svcd

These can be a pain on some peoples setups, but more so, on your stand-alone DVD player. Not all DVD players will play vcd/svcds, and some will play vcd but not svcd. There is a searchable database for DVD player compatibility here.

And a list here

For working with disk images of vcd/svcds (.bin/.cue, .iso, .ccd/.img/.sub) see the cd image section below.

For all your video needs check out www.videohelp.com and www.doom9.org. These guys know their stuff, and can help you with all kinds of media related questions.

.vob .ifo .bup
Video_ts folder
Usually these files will come all together in one folder called video_ts. This is a direct backup of a DVD's file system. Use Nero to burn them onto a dvdr by selecting "DVD video" from the DVD menu.

Audio

.mp3 .mp2 

Play them with WinAmp or your favourite audio player. Most new DVD players support the playing of mp3 CDs. Making mp3 CDs lets you put 100+ mp3 files on a cd for playing on your DVD player, computer, or portable mp3 cd player. However, they will not work on a regular cd player.

.ogm .ogg

Ogg Vorbis media files. You can find out more about them and download applications here. This file type is another encoding format that can be used for various media. You will probably want to download the DirectShow Ogg filter to play back OGM files. Any new version of WinAmp will also do.

.ape .flac .shn

These are music files which have been compressed using lossless codec's. This means that all of the original sound and frequencies have been retained. Most audio codec's, including the mp3 format are lossy codec's which discard certain frequency ranges in favour of smaller file sizes. For the free lossless audio codec or flac see here. For Monkeys audio codec or ape see here. For Shorten or shn see here, here, and , and here.
 

CD Image Files

.bin and .cue 

These are your standard images of a CD, and are used quite frequently these days. To open them you have a couple options.

You can burn them using Nero , FireBurner or Alcohol 120%, but this proves to be soooooooo problematic for a lot of people.

You can also use Daemon Tools, which lets you mount the image to a "virtual cd-rom", so basically it tricks your computer into thinking that you have another cd-rom and that you're putting a cd with your image file on it into this virtual cd-rom, it's great because you'll never make a bad cd again.

Alcohol 120% also sports a virtual cd-rom feature. Finally, if you're still struggling to access the files contained within any given image file you can use CDMage to extract the files and then burn them, or just access them from your hard drive.

You can also use VCDGear to extract the mpeg contents of a SVCD or VCD image file such as bin/cue.

.iso

Another type of image file that follows similar rules as .bin and .cue, only you extract or create them using WinISO or ISOBuster. Sometimes converting a problematic .bin and .cue file to an .iso can help you burn it to a cd. Examples of programs that burns iso's are: Nero, FireBurner and Easy CD Creator but there are many more!

.ccd .img .sub

All these files go together and are in the CloneCD format. CloneCD is like most other CD-Burning programs, see the .bin and .cue section if you're having problems with these files.

.cdi

These are Discjuggler image files. Alcohol 120% is able burn these. Daemon Tools and Alcohol 120% can mount them.

.nrg

Another type of image file created with Nero. As far as I know these are not mountable, except maybe by Nero. These are also apparently only usable by the version of Nero that created them. I don't recommend using these, as I've had nothing but problems with them.

.mds .mdf

These are media descriptor files created with Alcohol 120%. They are mountable using either Daemon Tools or Alcohol 120%.

.bwt .bwi .bws

I haven't really encountered these much, but some people still use them. These are Blindwrite image files. Use Blindwrite or Alcohol 120% or mount with Daemon Tools or Alcohol 120%.

Other Files 

.txt .doc 

These are text files. .txt files can be opened with notepad or whatever you default text editor happens to be, and .doc are opened with Microsoft Word. Be careful when opening .doc files from unknown sources, they may contain macro viruses. 

.nfo

These contain information about the file you just downloaded, and it's HIGHLY recommended that you read these! They will usually contain information regarding: the particular release group, the release date, the encoding method used (xvid, divx, vcd, svcd...) and format (ntsc/pal) for movie files; any cracks, keygens or cd-keys for applications and games; and various other pieces of important information. They are plain text files, often with ascii-art. You can open them with Notepad, WordPad, DAMN NFO Viewer or UltraEdit.

Unfortunately Windows uses this extension for it's system info program so simply double-clicking on the file probably wont work.

On Windows Xp

Right click on the .nfo file and select "properties"
click the button marked "change"
click "select the program from list"
click "ok"
select the program you would like to deal with this file type
check the box next to "Always use the selected program to open this type of file"
click ok.
Now any time you double click on a .nfo file, it will open correctly.

.pdf

Adobe Portable Document Format

Like Microsoft Word documents these can contain text, pictures and formatting. Unlike Microsoft Word documents, they cannot contain viruses, and cannot be modified.
Opened with Adobe Acrobat Reader.

.jpg .gif .tga .psd .png

Basic image files. These files generally contain pictures, and can be opened with Adobe Photoshop or whatever your default image viewer is.

.sfv

Checks to make sure that your multi-volume archives are complete. This just lets you know if you've downloaded something complete or not. You probably will only need to use this file type if you are downloading off of newsgroups. Because most releases come from the newsgroups, these files tend to show up on file sharing networks. You can open/activate these files with SFVChecker (Trial version) or hkSFV for example.

.par
.par2
.p** (where the asterisks are numbers)

These are parity files, and are often used when downloading from newsgroups. Parity files are usually posted along with the original files, with an index file at the beginning of a post and different sizes of volumes at the end of a post. These files can fill in gaps when you're downloading something from a newsgroup and get corrupted or missing parts. Open them with QuickPar.