The process can be referred to as video conversion or encoding. When you upload videos to Youtube all the videos are converted to flash video format and the file extension at the end of the name is .flv. You may have files that end with the extension.mpg, .wmv, .avi, or .mov on your computer. Each of these files are video files that can all be converted to a different video format. My favorite program to use is Magic Video Converter because of its easy to understand layout. However it is not a free converter. Magic Video Converter.

Follow up:

My trail ran out so I decided to look for a free service. I found that there are several free online services that will convert your video files to different formats but with an exception. The files must be uploaded and the files must not be bigger than 100mb.

Free Online Conversion

One of the best, easy to use, online video converters would have to be Zamzar. www.zamzar.com However the process can take a little longer that a program that is on your computer.

Total Video Converter

Another video converting program is Total Video Converter. This program is not as nice looking as Magic Video Converter but does convert several different formats. I once needed to convert a video format of a video I got from my phone via bluetooth. The format was .3gp and I was not able to do any video editing with it in Sony Vegas. With Total Video Converter I was able to convert the file to a usable format.
http://www.effectmatrix.com/total-video-converter/

Apex Video Converter

Apex Video Converter is another conversion video encoding program that is popular. Apex Video Converter offers conversion of many formats. Here is a list of what video formats it can convert.
http://www.tompegx.com/video-converter.html

Key Features of Apex Video Converter Pro:

AVI, MOV, QuickTime, MPEG, WMV, ASF, RM, RMVB, VCD, DVD to AVI, MPEG, VCD, DVD, MOV, RM, RMVB, WMV, ASF, iPod, PSP, 3GP, Xbox, PPC, PMP, Zune, Apple TV, iPhone, Flash SWF, Flash FLV, Youtube FLV, MP3 Audio, WMA Audio, WAV Audio, MP2 Audio, GIF Animation and GIF, BMP EPS, JPG, PCX, PSD, PDF, TIFF, WMF, EMF, PNG, J2K Picture formats.

As you can see there are several video converting programs out there and more that I have not mentioned. Choose which on you find works the best by trying out each of their trial versions.