Conditional moves are still played even in this electronic age. For example, Premium Members on LSS can send them. The opponent can't see them, but if he makes the expected move the reply is sent instantly. For a more complete discussion of conditional see Chessdotcom HERE.
In the old days one occasion when you might get “if” moves were in the opening. Modern Chess Openings was THE opening book that everybody used and quite often in games appearing in magazines, the MCO page and column was actually listed. So, when it became clear which MCO column the players were following one might send a series of “if” moves to the end of the line.
“If” moves were also common in case of a forced move. The thing is, sometimes players were wrong...the reply was not forced, or in the case of a series of if moves, a player could miss something. For example:
It could be that black had better moves on moves 29, 30 or 31 OR, one of white's moves was a blunder. I rarely used if moves for that reason...it was just too easy to overlook something. That's what happened in this old postal game. I had a strong attack but misplayed it and ended up a piece down with a lost position. My opponent saw what he thought was a crusher and sent me some if moves that were designed to lure me into his trap. I played along because I saw the refutation; he probably would have seen it too if he hadn't been in such a hurry to spring it and started sending me “if” moves!