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Why doesn't our solar system run into other solar systems over billions of years. There is plenty of time for it to be attracted by gravity to other objects. So I thought, it should be a common occurrence? or is there a reason it is not a common occurrence?

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Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

Douglas Adams, Hitchhikers Guide to the Galaxy

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Geeks think the same way. I was coming to quote the same line. But you should note that it's from Douglas Adams. –  dmckee Dec 5 '11 at 16:31
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