Vampire The Masquerade: Bloodlines
I can't make the patched engine.dll available for download as it is copyrighted software. But if you don't want to get your hands dirty with a hex editor you can now patch your game with these programs.
While revisiting these documents I found that I couldn't even reinstall the game because the MSI file uses a crude (and, indeed, incorrect) method to verify that the OS is supported. Following the instructions at PlanetAMD64 I was able to create a patcher that will correct the MSI.
If your game refuses to install, copy the contents of ALL the CDs to a directory somewhere, overwriting any files that exist on multiple CDs. Then run bloodlines64-install in that directory to fix your installer. Finally run setup.exe to complete the install.
bloodlines64-1.0 will patch the 1.0 version of engine.dll for you. It checks that the file is of the correct size before proceeding, so it won't break your game if you have applied the official patch.
This is the version available on Steam.
bloodlines64-1.2 will patch the 1.2 version of engine.dll for you. It checks that the file is of the correct size before proceeding, so it won't break your game if you haven't applied the official patch.
To apply the patch, launch the program and click [...] to open a file browser which you should point to the location of engine.dll. The patcher will then take a backup and edit the file.
If the program reports that the original file is the wrong size or doesn't contain the correct byte sequence then you either didn't apply the 1.2 patch to the game or something else has gone wrong. Your best bet is to reinstall the game and apply the patch in this case, as engine.dll changes with each version and even if you did obtain a fixed DLL it would probably not work.
Brad Jelinski reports that the v1.2 patch works for the Steam install of Bloodlines and that engine.dll is found under the Steam directory in steamapps\common\vampire the masquerade - bloodlines\bin. For most people, the Steam directory is C:\Program Files (x86)\steam.