If you are wanting to have folks send photos to you, then email really would be best. But...make sure they send you FULL SIZED files instead of letting the device (phone, etc) choose for them. You might get real tiny photos if they don't pay attention to that.
Yes, Dropbox needs to be installed for them to drop photos to you so I (personally speaking) don't see that as a viable alternative to most users (parents who might just use a smart phone as their only camera).
The problem might come (for you anyhow) in that people might have a myriad of different storage sites for their photos: flicker, smugmug, store clouds like Walmart, Walgreens, Costco, etc.  You would be roaming all over Hells Half Acre to get them. Why NOT let them send it to you instead where you can control where they go upon receipt?
Just my 2 cents.

Thanks for the quick reply.  I guess I thought that some people might have trouble emailing larger files?  And I don't know, will gmail stop my mailbox if we start getting a couple hundred photos that are all 4-10MB each?

I think a lot of size limits that used to be imposed on email servers have been raised (but I could be wrong on that). As for gmail, I have no idea as I don't use it too often. I don't think INCOMING size is important. They are stored on a cloud so you can get to them as needed. Gmail MIGHT have an overall size limit on storage but it has to be huge. I have an account that I rarely ever use and when I finally get around to emptying the thing out...it is massive in size. Literally hundreds and hundreds of useless emails (predominately ads).
Finally...you don't have to have that large of files to create a slideshow, so you can just ask them to send what they have anyhow. I'm guessing you will be getting a lot of smartphone shots too and those just aren't all that large so size shouldn't be an issue. For those using a regular camera, just request to keep it to 5MB or so. For a slideshow? I see no need for anywhere near a 10MB file, but that's just me.