.exe
Short for "executable," it tells the OS to run the program. Most Windows desktop programs use this extension.
.msi
For installation and removal of software within Windows. Opening an .msi file actually launches msiexec.exe, which reads the .msi file and does what it says. .msi files use Windows installer, so think of it as a standing for "Microsoft Installation.
.app
Executes a program within OS X (as .exe does in Windows)
.bat
Batch file. Used to execute multiple commands from the Windows command prompt (cmd.exe) within one file.
.scexe
Self-extracting firmware updates that HP produce, commonly associated with Linux machines.
.txt
Basic text file. Almost all word processors will open this, from the basic Notepad in Windows to Microsoft Word, and most other commercial and free apps as well. Generally, very few configuration options (such as fonts or inserting images) are available.
.rtf
Rich text format. A fairly basic document format developed by Microsoft and generally more compatible than .doc files.
.doc/.docx
Microsoft Word files .docx files are newer and support more features than older .doc files.
.xls/.xlsx
...
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.ppt
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.pptx
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.jpg
Called a j-peg, and sometimes you will see files with a .jpeg extension. The JPEG extension defines how images are compressed and stored. Very commonly used by digital cameras.
.gif
Graphics Interchangeable Format; uses a different compression standard than JPEG. Commonly used on websites.
.tiff
Tagged Image File Format; uses lossless compression, which preserves better image quality than JPEG or GIF.
.png
Portable Network Graphics; designed as a lossless compression format to replace gif. Very common on websites.
.bmp
Short for bitmap. One of the oldest and simplest image formats, usually for lower quality pictures.
.rar
Compression format introduced by WinRAR.
.tar
Short for tape archive, it's a format used in UNIX and Linux environments. It's not compressed; a compressed .tar file would have the extension .tar.gz.
.zip
The most common compression format, supported by most compression software.
.dmg
Mac OS X disk image files
.iso
Disk image archive files for optical media, such as CD-ROMs
.7z
Compression files generated by the 7-Zip program.
.gz
Compression files generated by the gzip program, which is mostly found on UNIX and LINUX systems. .gzip is the replacement for the compress utility.
.jar
Short for Java archive; similar in format to .zip files. Usually used to distribute software programmed in the Java language.
.mp3
This is short for MPEG-1 Audio Layer-3, and it's an audio-only compression format. It compresses files into about one-twelfth their original size yet maintains near-CD quality sound.
.wav
Waveform Audio File format; These are uncompressed files, and as such they have the best sound quality. They are the largest.
.flac
Open source compression format; not widely supported.
.aac
Advanced Auto Coding; produces better quality than .mp3, at about the same file size. This is the file format used by iTunes.
.m4a
This stands for MPEG-4 Audio, and it uses the same compression as .aac. Some media players wont play this file unless they are renamed to .mp4.
.mpg
These are compressed files commonly found on the internet. Most video players can handle .mpg files.
.mp4
This is an MPEG-4 file, or just a newer and better version of .mpg. Again, most video players can handle these files. It has the advantage over .flv of being supported natively on most mobile devices.
.flv
Flash Video; competing technology to .mp4, and requires a flash player plug in to play. Still a common format on Youtube and Google video.
.wmv
Windows Media Player
.avi
Audio Video interleave; Typically uses less compression than other formats. These files tend to be more universally supported than .wmv files.