Yes... until smartphone IM support finally offered competition that started to squash this particular aspect of price gouging.
Many people still "pay" for SMS. When we had outrageous per SMS charges (yes, also for incoming messages), carriers started to offer "bulk" -- e.g. 1000 messages per billing cycle -- plans and then "ulimited" SMS plans, typically for $30, $20, eventually $10 / month extra.
Now, more an more plans included "unlimited SMS". Not all, though, and total monthly bills that include such "unlimited SMS" vary widely. One also has to remain aware / beware of international SMS messages, where one's plan may still charge exorbitant per message fees.
P.S. Back in the days of high charges, just be so lucky as to end up on the receiving end of messages from some romantic interest who thinks your phone number is their interest's number. Obnoxious, perhaps crass messages, and to boot you're paying for the "privilege" of receiving them. (Fortunately, the carrier's limited blocking options sufficed to squelch those when he wouldn't believe I wasn't her.)