All you need is the standard European plug adapters (two round prongs). e.g.
One thing to look out for is if your hair dryer (or any other) plug is polarized -- one prong is wider than the other. A lot of adapters don't take this into account, so the slots on the input side aren't wide enough to fit the polarized plug and you have to really force it. I had this problem with my travel dryer and some other plugs around the house. It's most common with the cheap little adapters like this:
Another thing to consider is that most outlets are grounded, which means they're inset into a circular gap:
If the prongs on an ungrounded adapter don't fit exactly right, and you have a fairly heavy plug (like the little block for an iPad charger), it can pull the plug out of position so that it loses the connection.
The little ones are great to throw in your luggage because they're tiny, cheap, and lightweight, but it's worth having at least one grounded or more solid adapter just in case.
You can find the kind in the top picture pretty cheap from all kinds of internet electronics sites (dealextreme.com, Amazon, etc). They're not that high of quality, but they work fine and stay in the sockets. I've owned a few dozen of them (almost all of my electrical items at home run through plug adapters) and I've only had a problem with one. I could even use it to hold my hairdryer plug into a vertical outlet:
If you don't have a polarized plug, they're great. If you do have a polarized plug, a lot of them might not fit it, in which case I'd recommend going to a local shop (Fry's, Radio Shack, etc) to check them out in person first.
On a few very rare occasions, I've run into non-grounded outlets (mostly at a home or office), so I like to have both kinds just in case. Usually the grounded version is enough.