Rectangle uses int coordinates.
Rectangle2D is an abstract class that doesn't care if you're using int, double or float coordinates.
If you need the greater precision of double and float, you'll have to go with Rectangle2D.
Rectangle2D is the base class, so if you're writing code that operates on rectangular shapes in an abstract way, go for Rectangle2D, and assign it like so:
Rectangle2D rect = new Rectangle2D.Double(double, double, double, double);
or
Rectangle2D rect = new Rectangle(int, int, int, int)
If you know you're only going to deal with ints, you can use Rectangle all the way.
You might say that Rectangle should be called Rectangle2D.Integer. But that's not quite it either, because e.g. Rectangle is the only one of the three that implements the serializable interface.
Like skaffman commented, it's a bit of a legacy issue.