I've been delaying all summer the search for a new free webhost, knowing how frustrating and time consuming it can be. I'm quite happy with Zymic.com (6000 MB space, 50 GB bandwidth), but I already have four websites hosted there and I didn't want to push my luck.
My new discovery is Hostinger.ro. The free plan includes 2000 MB space, 100 GB bandwidth, FTP, PHP, MySQL, and bilingual control panel in both English and Romanian. There's a limit of 20,000 files, but other than that I didn't notice any restriction that might bother me. The upload went fine, and the sites are loading in a reasonable amount of time. I already moved three sites and I'm considering moving other four. It's too soon to tell if the promised uptime is real so I'll keep an eye on that.
For free domain names, I'm using dot.tk. Some keywords are flagged and reserved for the paid subscription, but it's easy to find a combination of words that still works. The maximum free subscription is 12 months, and it can be renewed.