SeaUrchin
I am Indian born in London, parents born there, and have made many visits to relatives over the years. On one particular trip my husband came with me - his first visit to India.
I remembered when visiting with two (white) girl friends some years previously a number of people had asked them to have their photos taken with them so I had warned my husband to expect this.
So when a school girl came up to us with camera and smile I gave him a told you so grin... only to have them take their photos with ME!
I'm an overweight and very ordinary looking character so I couldn't work it out at all, I could only assume I looked like someone famous or something. Poor woman!
;)

Should explain, husband is (white) English and 6 foot 6 inches tall so stands out like proverbial sore thumb in India...

I've always asked Blonde Japanese girls to take my photo with my Costco $7 disposable camera. They always put their hand up palm out and giggled. Have a good time Muimei and beware of young men wearing running shoes'

Ask someone with a nicer camera then the one your handing over. That should alleviate the fear that they will run off with it. Also, with a bit of luck (and this is why I'd pick someone with a really nice camera), they might just know how to use it well.
Good luck.

perhaps those who are nervous about handing over their camera to a total stranger have been watching chevy chase european vacation in preparation for their trip!! yes i do it all the time and also offer to take photos for others too, it is a touristy thing to do, but i usually ask other tourists in preference to locals, mainly cos i think locals could be rushing off to business etc. i must say though that i often wonder when tour guides get us to line up our 30 odd cameras on the groud and take the group photo, how we would ever retreive our cameras if someone did come by and steal one. it woudnt be mine because i am not even into digital camera taking yet!!!

Yes, plenty of time. I usually try to ask a family (one of the parents or their teenage children) or a couple with cameras in their hand, to take my picture and I'll take their pic in return, and it has worked out great.

But keep in mind also, try to select someone that seems like they know how to take pics, otherwise, you'd waste your time. I know it sounds stupid but I have experienced also seeing my pics out of focus etc. Thank God for digital camera so at least you can ask someone else to retake it.

A tripod and self timer can work wonders - also increases the sharpness of your shot.

Strangers are often kind - if I'm travelling alone and must have a photograph of myself I usually ask a respectable looking passerby to assist.

I haven't traveled solo thus far, but one of my sweetest memories is of strolling on the University of Washington campus with my son in his cap and gown on his graduation day, when he approached a couple where we were standing in front of Denney Hall, and said "Would you take a picture of me and my Mom? She's the reason I'm here today."

It brought tears to my eyes then and still does when I remember the moment.

That said, when I am traveling, I rarely wish for photos of myself and am not enamored of the few I've had taken. I take photos of my sister/travel partner, but the only ones that seem to please me are those that capture HER image, not the image of her posing in front of some monument or another. I have great pics of her sitting across the table from me on the terrace at Hotel Haus Lippman in Beilstein, with just a hint of the overhead grape arbor fuzzy in the background, or of her seated across from me on the train from Rome to Milan.

All my favorite photos I've taken are about a place and a moment for me to remember, the world through my eyes, not me through someone else's eye.

We have asked people plenty of times and had them offer, too. For several years now, when someone takes a picture of us, I thank them and then ask if I can take a picture of them so that I can remember them and their kindness. Everyone has always agreed, and those are some of the best pictures and memories we have of our trips. People tend to stay for a few minutes after you take their picture and talk with you. Having a picture of them helps you remember the occasion (where you were, what you were doing, what you were taking a picture of, what you and they talked about, etc.) so much better. Also, when they have been locals, many times they have given us great tips about what to see or where to eat in the area.

Thanks, all of you. Great advice and stories! I'll definitely watch out for young men with running shoes! :D I guess I was quite a bit paranoid about going to Europe... Way too many "horror stories" relayed to me by family and friends. I was a psych student and still wasn't thinking with my brain! All my relatives and friends seem to only think about the bad stuff. I got more info about thefts than info about great places to see!

Thanks for setting me straight.