In how many points can two circles intersect?

I only see 3 intersection possibilities :

1) The two circles coincide, that is, they are one circle on top of the same size circle with the same center. Those would intersect at all points.

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2) The two circles 'cut through' each other, like you sometimes see in Venn diagrams. In that case, there are 2 points of intersection. Here's a picture of what I am describing:

http://www.google.com/imgres?q=intersecting+circle...

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3) The two circles touch (intersect) at only one point, like this :

http://www.google.com/imgres?q=tangent+circles&sta...

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The only other 'intersection possibility' that I can think of is that the circles do not intersect.