Well you have Wikipedia on IPFS, but it's read only. The issues are described here: https://ipfs.io/blog/24-uncensorable-wikipedia/
Making read-write or having databases on IPFS is harder. There is an experimental database using IPFS: https://github.com/orbitdb
Possibly using Tor or I2P. There is also a way of using Tor+IPFS, but I don't know about the state of implementation.
I don't think there is any popular implementation yet. Maybe an interesting app is OpenBazaar, a kind of decentralized eBay.
It's good if you would have some huge datasets that you would like to share with lots of parties (for example in science). No idea what else.