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Unlike lossy compression, lossless is a mathematically perfect way of representing your audio data. After decompression, you will have a bit-perfect copy of your original wave file - just as the name states, it is without loss. You can think of the various lossless compressors as highly tuned versions of Winzip or Winrar that are specifically for audio.

Lossless compression explained

Popular lossless formats

Note that currently no single format can be considered best for all applications. Rather, the best format depends on the intended use, as well as a number of other factors (such as licensing and file structure). For example, Shorten and FLAC are widely used for sharing live music because of their cross-platform support and speed. Monkey's Audio is popular among Windows users for its slightly more efficient file size.

Lossless compressors comparisons (note the specific assumptions and limitations of each comparison; in particular, results are sensitive to the music selected):

Includes an interesting graph of encode/decode speeds vs. file size on the All Albums page
Lossless comparison 
A comparision focusing more on codec features and less on absolute encoding efficiency. Also features a table comparing most popular codecs based on their features.
Performance Comparison of Lossless Audio Compressors - Compares file size, encode speed, decode speed for APE, FLAC, LPAC, WavPack, Shorten (SHN), RKAU, OptimFROG, LA, WMA Lossless. Updated 5-2003
Includes a variety of notes, but the testing was completed in 2000, making the results largely obsolete.

See Also