HelioHost is probably the only free webhost I know about that is actually a 501(c)(3) nonprofit. It's run completely by volunteers who are passionate about good webhosting and have the technical know-how to pull it off.
And boy, do they ever! The HelioHost team doesn't rent any hardware, they own all the servers they operate, and they are constantly reinvesting donated funds to upgrade their hardware for their customers. They provide an unprecedented level of services that even paid hosting struggles to beat (unlimited bandwidth and email accounts, nearly a full GB of storage space per account, ~99% uptime, etc.)
But what keeps me with HelioHost ever since I joined them some 5 years ago is their incredible customer service. The team actively responds to customers on their forums and are flexible enough to accommodate most requests. They personally monitor your sites for malware and move fast to secure your sites for you, unlike most paid webhosts that only respond when someone complains. Recently, my WordPress site was compromised by a cybercriminal attempting to phish Chase bank customers, and HelioHost secured my account a full hour before Chase's security firm had time to email me about it.
I'm very, very impressed with HelioHost. They are a free host that not only manages to keep up with the big, premium paid services, but actually outperforms them. HelioHost, consider yourself on my list of supported nonprofits.
Tip for consumers: Folks have started to hear about HelioHost and they're becoming a lot more popular; it can be hard to sign up for a free account before the daily quota fills up. This isn't their fault; they need the daily quota to negotiate the load on their servers. To get an account on their flagship server Tommy, you can donate a couple of bucks and receive an account on the server as a thank-you gift.