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.