Well, first, let me assure you that the Sun has no intention of doing any such thing. Only stars that weigh considerably more than the Sun end their lives as black holes. The Sun is going to stay roughly the way it is for another five billion years or so. Then it will go through a brief phase as a red giant star, during which time it will expand to engulf the planets Mercury and Venus, and make life quite uncomfortable on Earth (oceans boiling, atmosphere escaping, that sort of thing). After that, the Sun will end its life by becoming a boring white dwarf star. If I were you, I'd make plans to move somewhere far away before any of this happens. I also wouldn't buy any of those 8-billion-year government bonds.
But I digress. What if the Sun *did* become a black hole for some reason? The main effect is that it would get very dark and very cold around here. The Earth and the other planets would not get sucked into the black hole; they would keep on orbiting in exactly the same paths they follow right now. Why? Because the horizon of this black hole would be very small -- only about 3 kilometers -- and as we observed above, as long as you stay well outside the horizon, a black hole's gravity is no stronger than that of any other object of the same mass.
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