However, there are limitations to its use that don't occur with some verbs.
For example, if you have a book, you can't say "I'm having a book".
Here are some correct sentences:
"I can't answer the phone; I'm having a bath". (AmE. uses 'taking' here)
"Tomorrow I'm having a blood test". (ditto, I believe)
"My wife is having a baby. This sometimes means she's pregnant, and sometimes it means she's actually delivering it".
"Your English is good. Have you been having lessons?"
"He's having a fit. (he's epileptic). He's having an asthma attack".
"I'm having a hard time with this test".