If the game crashes constantly, like it did for me, there is a quick way to get around it. I can't say for sure that this will work for everyone, but it worked for me. It did work on both the Sold Out and retail versions.
1. Install the game from the CD as usual.
2. If you have the retail version download and install the patch (the Sold Out version is already patched):
Mirror 1: http://www.megaupload.com/?d=D74W66CJ
Mirror 2: http://www.4shared.com/file/LwtzSmAg/hitman_sp1aUK.html
Mirror 1: http://www.megaupload.com/?d=8AGCQ85V
Mirror 2: http://www.4shared.com/file/nNfav5Jq/hitman_sp1.html
3. Run the game setup, either from the start menu shortcut or the exe in the game install folder (usually C:\Program Files\Eidos Interactive\IO Interactive\Hitman - Codename 47).
4. In the Available Renderers drop-down box select OpenGL and your resolution.
This should fix the random crashing issues.