I may have nissed it, but i didn' t see anyone mention that there are two superficially similar Dvi connectors. One has 4 more signals than the other, arranged as a cross at one end of the connector. These are rgb and hsync . Vsync is somewhere in he other big array of pins, because four is simply not enough. The other type has a flat wide pin only. I can't remember the precise difference between them, but there is a wikipedia article that explains it.
As several people have pointed out, the second type needs some heavy lifting to convert, but the firs is simple, just wires. Pinouts are on the wiki article.
There are chips which do this from silicon image among others, but they are big evil and unapproachable no fab ip only companies, whose first question is: How many million pieces a year will you be needing?