My daughter and I are visiting Athens in June and would like to help out at a refugee camp or something while we are there. We would also consider collecting items to deliver there. Has anyone had experience doing something similar?
Frankly, I don't think you'll find this plan to be very practical or feasible. You might find something of interest on these web sites, such as a way to donate money.
Try contacting your country's embassy in Athens for information about volunteering. If you're American here's their contact info: http://athens.usembassy.gov/contact.html
I'm thinking along the same lines as Laura. While the heart is in the right place, volunteer work as a side activity of a leisure trip isn't very practical for all sorts of reasons. People who go on volunteer missions usually do them through non-profit organizations which help manage a lot of the complexities, and length of service tends to be measured in weeks rather than a couple of days. It can take too long to bring a very short-term volunteer up to speed.
Special skills are often preferable as well: language; medical; engineering; disaster coordination; security; etc.
Bringing items also isn't especially practical as hauling it all over creates a luggage-weight problem, and often the types of things MOST needed can't be carried in a suitcase: water, food, medical supplies, vaccines, fuel, tents, etc. Most critical needs can also change very quickly. That said, giving to an aid organization which has the ability to buy in bulk and have it shipped and distributed quickly is probably more effective.
There are always people close to home who are in need, and who would be very happy for your help! If you're truly interested in an international mission abroad, I would look into volunteer efforts through organizations which manage some of the logistics, and provide some training on what needs to be done in advance (such as immunizations), what tasks you'll be performing, and the types of conditions you'll be operating under.