I've installed a popular board mod called "ReIMG", which acts to resize posted images that are too large. It will scale them to within the allowed dimensions, but place a magnifying glass icon in the top left corner. If you click on the image it'll bring up a full-sized version in a light box.
I've set the maximum allowed dimensions (before it will be resized) to 800 pixels wide by 600 high. If you feel something else would be more appropriate, please post your feedback here.
Example, which is actually 1024x768:
Also note that if you have javascript disabled in your browser, then it should still resize them (I think) but it won't offer you the option of viewing the full-size image. Or maybe it doesn't even resize them, I forget.
As for signatures, I wish there were separate options for signature dimensions but there are not. Our signature limit policy is 800x300. As a result, it will correctly resize sig images over 800 wide, but will still allow ones over 300 high, up to 600 high. I'm looking for another way of catching these, rather than having to manually police signature sizes.