You can have and use uncompressed video... if you have LOTs, really LOTs of storage space! That´s why most digital video you find is compressed in some way. More than simply compressed, video is really encoded by a codec and then saved in a file following a certain format.
Codec vs Format 
Codec means "encoder/decoder". It is a software which compresses the video for storage purposes with a certain algorithm, and sometimes (not always) can decompress the video for playing it as well.
It is very common that people confuses the codec with the file format of a video. There are, indeed, some file formats which require a specific encoding standard. However, this does not mean that only one encoding/decoding software must be used --- there are lots of encoders for MPEG 1 video files, for example. And, more than that, there are file formats which can "store" video compressed in a variety of ways.
The very common AVI file format is an example --- it can store uncompressed video, or video which was compressed by, just to mention one example, an MPEG4-standard codec like XviD, DivX, etc. You may hear people talk about "this DivX video" or similar, but this is not precise --- in fact, a video compressed with the DivX codec is really a MPEG4-standard video, and as such it can be played by any other MPEG4 decoder, like XviD.
Some problems arises from the fact that the AVI format uses an identification string called FourCC which is used to tell which codec was used for compressing the video. Some applications made for a certain compression standard may refuse to work with a different FourCC code even if the compression method is the same. And people often take the FourCC information as the "format" of the video.
So, to make things clear: codec is the software which compresses video; and there can be lots of codecs which output files in the same format.
Common video compression methods and codecs 
- DV: used by DV videocamcorders.
- MPEG-2 : used for DVDs and broadcast digital transmissions.
- MPEG-1 : used for VideoCD.
- H.264 / MPEG-4 / Avchd: ISO/IEC standard advanced video codec.
- DivX : video codec well-known on the Internet.
- XviD : Open Source MPEG-4 compatible video codec.
- theora : high performace Open Source video codec.
- WMV: proprietary Microsoft Windows video standard. Used for internet streaming, it was designed to compete with Realvideo.