Greenshot has a feature like that, but you need to have Microsoft Office installed.
Take a screenshot of the desired area (using the Print Screen key).
In the resulting menu, select OCR.
The resulting text will end up in your clipboard. As an example, here's the result of me trying it on your post:
Sometimes. I find myself typing out a lot of text from a screen capture Its quite tedious
Is there an OCR (Optical Character Recognition) program out there that would allow me to quickly convert the something like a screen capture. or the contents of the Windows clipboard (a bitmap), into text?
If you already have the image in your clipboard, you can run the OCR on it by clicking the Greenshot icon in the notification area and selecting Open image from clipboard.
This will then open the same menu shown above.