Dropbox is free but it has a storage limit so you can use without upgrading to business (you just invite users to access your folders by email) but you'd need to move the pictures somewhere else as they come.
You could have people upload to their own Dropbox and share the folder with you so you'd see all of the folders in your own Dropbox but each folder would be using each person's own storage limit, it's a tiny bit more work for guests but it means you aren't limited in terms of space.
If you are using the desktop app the easiest way is to choose "New shared folder" on the right, name it and type people's email addresses in to share with them, they will then be emailed access to the folder which they can drag and drop files to. If they don't have Dropbox they will be invited to join for free. Like I said though, there's a storage limit so it would be more sensible to have each guest make their own folder and share it with you. If you don't want to get them to do this then you will need business to upgrade the limit.
You could also do much the same thing with Google Drive, anyone that has a gmail email address will have this for free and can share folders with you in the same manner but again the storage limits could be problematic unless each guest uses their own account.
Another option would be to create a closed Facebook group and have people upload albums there so anyone not in the group won't see them. Facebook doesn't really have limitations so it's an easy option that most people can access.
There are alternatives to Dropbox out there but mostly they will come with a cost, it's the storage limits that are the real issue.
Cloudup looks ok (I haven't used it but heard good things), the limit for free is 1,000 items so may work for you depending on how click happy your guests get - cloudup.com/