It seems we just can't have enough bumps for this.
It's simple: Your entire signature should be no bigger than 700x250 pixels. If it's too big, we will change it according to our own whim, immediately. This is already a huge size so if you can't fit what you want to in there, you're doing it wrong(ly).
If your images are oversized, you can make use of the scaling feature. That is, instead of just [img] tags, you can use [img=700x250] or any dimensions to scale your image. This means there are no excuses for oversize sigs as a result of image size.
If you have a GIF in your sig or posts, please check that it is 1MB or under.
Since I've stumbled across quite some oversized signatures lately, and people who didn't know that the 700x250 maximum size include images and text, I'll give this yet another bump to solve the confusion.
If you want both images and text in your sig, remember that one line in standard size is ~17px. As example, for myself I've figured out, that the perfect image size is 700x200 so you can fit 1-2 lines text/links beneath it.