The short answer
The complete lack of atmosphere means that all of the air in your lungs tries to escape since there is a pressure difference between the inside and outside. The effects can be similar to the bends, where gases dissolved in the blood can expand and accumulate in joints. There can be some slight swelling (mostly painless and reversible) of the skin. Tests on animals and accidents have shown that people will lose consciousness after 10-15 seconds. Interestingly, on 1 occasion, the subject reported that the saliva boiled off his tongue.

For prolonged exposure (the time it takes to starve the brain of oxygen) there is death.

What won't happen

Your blood won't boil away out of your veins!
Blood is a fluid and as such does not change volume (by much) with changes in pressure with changing state (into a gas). Since blood is contained inside the body and not exposed directly to the vacuum you can expect not to boil.

You won't instantly freeze.
To freeze, you need to have all of the heat in your body to be drawn away. If you think back to your science lessons in school, you'll know that there are only 2 ways to transfer heat away from a body, conduction and radiation. Space is cold, but there is also nothing there so you wouldn't lose any heat from conduction (as you would in an atmosphere). You would lose heat by radiation, but in practice this isn't very much when you look at the amount of time you're actually going to care about it!

No, your eyes do not pop out of your head.
Once more, this is to do with fluids not expanding.

You could get severe sunburn!
Ok, perhaps this should be in a different section. In space, you are pretty much naked to the sun without the atmosphere to protect you. If you are in direct sunlight, the intense UV radiation will give you something to think about!

Has anyone ever been exposed to a vacuum?
Yes. When doing some tests in a vacuum, the suit worn by the subject sprung a leak and he was exposed to (near)vacuum. He lost consciousness after 14 seconds. The suit probably did not reach total vacuum since the test chamber was repressurised very quickly.
Another incident involved Joe Kittinger on his historic balloon ascent. He lost pressurisation to his right hand where it became painful and useless. It returned to normal as he returned to earth and air pressure became gradually normal.

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