Lots of really good input on this one so far.
My approach to capturing images is dependent upon the goals I have.
My position on this is that I'll do whatever's necessary to create the image I want. That usually means putting a tremendous amount of effort into getting the capture as good as possible in camera (more on that, below). But it also includes whatever I feel like doing in post. (more, below). So I do a combination of both, with a priority on the capture, and then backup support from editing.
Getting it right in camera, for me, means capturing the highest quality possible, from a technical standpoint as well as an artistic standpoint. For example, getting as close as possible to the subject (usually wildlife or macro...and getting close ethically, mind you) to avoid having to crop significantly. Less cropping means higher quality in most cases. Do I account for post processing cropping options by not always filling the frame? Sure, when appropriate or needed. It all depends on the situation. Then there are things like sharpness, shutter speed, DOF, lighting, and the list goes on. All important to me to get right in camera.
The biggest one for me, as a fine art image creator, is the clean background and lack of distractions. I'll do whatever I can in the field to get that. I'll plan for it, scout locations, decide when I should not shoot, move around and position myself for a clean background, lay on the ground, etc. The advantages to getting the background right in camera are: More natural looking result, higher image quality, less time spent in post processing, etc (changing or blurring a bg behind a wildlife or macro subject can often be extremely time consuming, challenging, and may not always result in a natural looking and high quality image.) To summarize, for me, getting it right in camera is about making the highest quality fine art image possible. And I often make close up portraits of birds and other detailed subjects, requiring all of these technical things to be done well in camera.
On the other hand, I'll do whatever I want in post processing to create the image I want. I create art, not documentary images. So if I did everything I could in the field, but still couldn't get everything "perfect" I will do something about it in Photoshop. The main point, which others mentioned, is that I'm using it as a tool to polish the best shot I could capture, not as a crutch to fix a lack of skill, or laziness.
It's all about knowing what I want to create and then doing what I need to in order to make it happen. That's it.