
Theme Hospital is a game by Bullfrog, released in 1997. In the game, you build and manage a hospital from a 2d isometric view, treating patients with funny diseases such as "Bloaty Head", "Transparency", "Spare Ribs", "Hairyitis" etc. etc. Have a look at its wikipedia page for more information.
CorsixTH is a project which aims to recreate the gameplay of the original and improve some aspects dearly missed in the original, such as the ability to run natively on modern systems (windows xp/vista/7, linux, mac osx), higher resolution, fixes to various bugs, etc. CorsixTH is coded from ground up in a mixture of C++ and Lua, but requires (similar to OpenTTD prior to the graphics/sound replacement) the original game data of Theme Hospital to run.
Current release is Beta 6.
YouTube video of Beta 6
The rest of this post is obsolete

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Today, as a little christmas present to all fans of Theme Hospital / classic games in general, and also to celebrate 5 months of development, "playable beta1" was released. Binaries are available for windows (32bit / 64bit), users running different systems currently have to compile themselves (see HowToCompile on the wiki).
The game is currently in a minimal playable state, you can already build a number of rooms, hire staff, watch some patients getting diagnosed and treated, either happily leaving the hospital again (with of course a few bucks less in their pocket), or sometimes, if the doctor or nurse messed up, kick the bucket.

Links:
Project Page
"Getting Started" wiki page
YouTube video of playable beta1