Can bitcoind still do CPU-based mining or was that feature removed? I'm seeing conflicting claims about whether  bitcoind can still do CPU-based mining. As far back as 2011 people were saying that feature was going to "soon" be removed. Was mining removed?
By the way if mining is removed from bitcoind, what are the things it can still do?
It is still there as of version 0.8.5, but just a reference implementation. It's not optimized, doesn't support pooled mining, and is not exposed via the Qt GUI.

To enable, start with the -gen option. But other than testnet (and even there...), it's utterly pointless.