Basically, I'm coding a 2D platformer engine, since I'm sick and tired of writing one everytime I want to code a new game and I just end up ditching the whole thing. I want to concentrate more on the content.

Anyway, what are the best methods of calculating and handling rectangle to circle collisions? Like, for example, when a giant boulder hits the player. Or something.

Assuming solid shapes, you need to handle the circle being inside the rectangle.

Go check out an open-source 2D physics or collision library. Copy->Paste->Profit.

Do you mean the circle skips over the border of the rectangle entirely in one logic loop? Or skips over the entire rectangle during one logic update? It would be better if the location of the circle from one logic loop to the next logic update were defined as a line segment itself, and test for collision between this line segment and the rectangle. I figured this out many years ago when playing Need for Speed and you could run over a spike strip without damage if you were going fast enough.

[EDIT]

This would be helpful as far as simulating the radius for this line segment. Even if the game isn't 3d, you need to see if the mid point of the line connecting the two circles (in time) gets within the radius of a corner of the rectangle.

http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/

I still stand by what I said regarding the circle completely skipping over the rectangle between logic updates. In the "real world" the circle would have necessarily passed through the rectangle, and been inside at some instant.