Some beautiful rules can be applied every time you see certain combinations of numbers, regardless of what squares have already been cleared around them.
These interesting cases will always tell you where three mines and three safe squares can be located. The 1-4 is most common; the 2-5 less so, and the 3-6 even less so (there's even a similar 4-7, so rare it's not even worth showing):
This one I stumbled across after years of just playing right through it. I ran a computer verification for it and it turned out even better than I had realised. It doesn't matter what you already have cleared around it -- wherever you see a 1-3-2 combination, you are guaranteed eight clear squares, and two mines flanking the 2.
Though usually along a wall (see the 1-2-1 in the Basics section), this rule can be generalised -- like the 1-3-2, wherever you see this combination, all these eight squares can be cleared: