Yes, dial *67 (1167 for rotary phones) then the number you wish to call. There may be a per-call charge associated with this feature. Some phone companies also allow you to subscribe to a feature that always blocks your number, as well.
True, but at least with Qwest, I just called them and had my ID blocked. No charge.
Then, sometimes the person I’m calling has the feature you mention, but if you still want to call, you just hit *82, then dial the number again and it bypasses the call blocking you have for that one call. I expect most phone companies have this.