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...except that your ISP may limit the size of your outgoing mail...so check into that before you try sending a xxMB file or folder.
...and you might find organizing them and accessing them easily may be a bit of a hassle.
There's alot of "online file storage" sites that charge money, as you know, but a cheap (not free) alternative to them would be to get web hosting and ftp files to your server.
GoDaddy has 5GB for $75 every two years (or $43 for per year).
[I don't use them, so don't endorse them for site hosting]
Personally, I think you would do better if you have a CD-R or dvd burner in your computer. You can burn your files to a dvd or CD-R. My own CD-R burner was less than $50 US, and I keep all my backup files in that manner.
Best of luck.