Well, for starters, you wouldn't be able to breathe!   In Earths atmosphere, 78% is composed of nitrogen, while 21% is composed of life-giving oxygen, so every breath you take would not have one of the most important elements known to fuel life.  Another thing that would occur if the Earth had no atmosphere is we would be bombarded with all kinds of incoming space debris.  This debris normally burns up when it enters the atmosphere, and rarely makes it all the way down to the Earth itself.  If you would like to see what the Earth would look like, take a look at the moon, with all its craters.  Those craters are the result of objects hitting the moons surface.  Another thing that would happen if the Earth had no atmosphere is the oceans would boil away, leaving no water here on Earth because there is not atmosphere to help complete the water cycle.  Admit it, you just got thirsty, didn't you?  And then, theres the problem of being the recipient of all the harmful radiation from the sun that the atmosphere normally takes care of.  The ozone layer would be nonexistent, so every time you wanted to go outside, you would have to either put on a radiation suit, or use a sunblock that has a solar protection factor of 3000!