Outlook.com – Microsoft’s free solution, if you have an office 365 or have purchased Microsoft Office in the last 5 years you may have a mailbox already. 34MB file attachment limit.
GMX.com – Another free solution that allows you to send files up to 50MB
Yahoo.com – Oldie but a goodie, 25MB file attachment limit.

Additionally this one might be your best option if you do not require bells and whistles. Most, if not all Internet Service Providers offer multiple free email accounts with your ISP account.