Why do Humans not produce Vitamin C like other mammals?
Humans do not produce Vitamin C due to a mutation in the GULO (gulonolactone oxidase) gene, which results in the inability to synthesize the protein.  Normal GULO is an enzyme that catalyses the reaction of D-glucuronolactone with oxygen to L-xylo-hex-3-gulonolactone.  This then spontaneously forms Ascorbic Acid (Vitamin C).  However without the GULO enzyme, no vitamin C is produced.

This has not been selected against in natural selection as we are able to consume more than enough vitamin C from our diet.  It is also suggested that organisms without a functional GULO gene have a method of "recycling" the vitamin C that they obtain from their diets using red blood cells (see Montel-Hagen et al. 2008). 

A 2008 published study (Li et al. 2008) claimed to have successfully re-instated the ability to produce vitamin C in mice. 

Simply as trivia: other than humans; guinea pigs, bats and dry-nosed primates have lost their ability to produce vitamin C in the same way.  



References 


Li, Y., Shi, C.-X., Mossman, K.L., Rosenfeld, J., Boo, Y.C. &amp;
Schellhorn, H.E. (2008) Restoration of vitamin C synthesis in
transgenic Gulo-/- mice by helper-dependent adenovirus-based
expression of gulonolactone oxidase. Human gene therapy. [Online] 19
(12), 1349–1358. Available from: doi:10.1089/hgt.2008.106 [Accessed:
31 December 2011].
Montel-Hagen, A., Kinet, S., Manel, N., Mongellaz, C., Prohaska, R.,
Battini, J.-L., Delaunay, J., Sitbon, M. &amp; Taylor, N. (2008)
Erythrocyte Glut1 Triggers Dehydroascorbic Acid Uptake in Mammals
Unable to Synthesize Vitamin C. Cell. [Online] 132 (6), 1039–1048.
Available from: doi:10.1016/j.cell.2008.01.042 [Accessed: 31 December
2011].