There are plenty of options depending on what you want and how big your file is.
If you have a Google account you can use Google Docs, which will allow you to upload files up to around 10 megs. I used to do this for my GEDCOM files.
You can also use a backup website such as Dropbox. This is what I use now. You can upload any type of files you want and I think you get 2 gigs for free. The only problem I have had with this is that it seems to think that some files that are too small are text files and will try and open them as such. This doesn't happen on all computers so it must be something on one or two. It's still easy to get around.
Both of these solutions are not OS dependent so you can use a PC or a MAC.
You should think about another way of using both computers if you can without using GEDCOM. GEDCOM works ok, but it is not the best idea as you can have problems. You shouldn't lose basic information, but you most likely will not have any media links and there can be problems with sources and citations, you will not lose them, but the formatting can go a bit bad.