There's no more 100% free with no banners. But you can find many that have catches (ads, pay after 1 year, etc...)
I suggest godaddy. There are a few that are a little bit cheaper, but they really don't compare to godaddy's control panel and customer service (if you ever need it). The final price at godaddy (without any discounts or deals) is usually $9.20/year (including ICANN fee).