Tarantula hairs are really more like hollow tubes but are called hairs, because they look like hairs. This type of hair is called urticating. Urticating hairs can also be found on certain caterpillars (processional caterpillars in Spain) but you are probably more familiar with them on stinging nettles. All new world tarantulas have them, but there are different types. (just to clear up something Hadge wrote above, old world tarantulas are in Asia but also can be found in Africa and Australia)
You can read more about the hairs here
http://en.wikipedia.org/wiki/Urticating_hair#Urticating_hairs_in_tarantulas
This is what the different types of hairs look like
My Theraphosa apophysis (the one which can grow to 28cm -30cm) probably has the worse type and could be fairly medically significant, especially if the got into my eyes, as this could result in long term treatment and possibly permanent damage.
Others such as the Brachypelma boehmei above do kick their hairs but they are not so bad. I have once been hit by some hairs from a Brachypelma and the result were cold like symptoms. The hairs on the skin result in a rash and itchiness. I didn't get them in my eyes.
The good news is old world tarantulas don't have urticating hairs and so don't have this defence mechanism. The bad news is they tend to make up for that with more potent venom.
However venom potency can be a bit if a tricky area. Not all bites will include venom and it depends on how defensive the spider is being to how much it will inject. Some could produce one bite while others could give you multiple bites in quite succession.
I should point out that because tarantula venom if quite pure NO-ONE HAS EVER DIED DUE TO TARANTULA VENOM. However some old world species could make your nauseous, produce severe cramps, fever, dizziness etcetera. Also some old world species venom also contain a very similar chemical to chillies in their venom, just so you know you have really been bitten.
The best way to avoid being bitten is, don't handle them. There are some "beginner" species like this Grammostola pulchripes
Which have very mild urticating hairs, very mild venom (no worse than a bee sting) but a very mild temperament too. My G.pulchripes has never tried to bite me or even hinted it has any intention to do so. She is so docile, has never become agitated or threatened and so never seen me as a threat. When I feed my spiders I leave the lid off her enclosure and let her wander round the room, if she likes. She is so gentle and slow I can just scoop her up if she wonders too far.
I have never been bitten but have read quite a few bite reports. Some can be pretty bad but most mild to humans. I would rather be bitten by my G.pulchripes than say a more common pet like a dog.
That's the bad stuff about spiders, the good is rather endless. if you keep them well and as natural as possible you get a small window to watch a fascinating creature live naturally and well, and they can be both stunning and very, very odd.
