Before trophies I just played the game to beat it and that was it. I saw no reason to do things like side quests, mini games, or collect collectibles. Trophies let me see all my games in list form on one screen and see an exact % of how much I completed in each game. I wish a system like this was available in the old days and I also wish Nintendo would implement a similar system as well on the 3DS.
TBH trophies haven't changed much for me. I complete some games way more than trophies would even note. Other games I can't even be bothered because I completed the biggest challenges, I don't care about a trophy that says fight 17k battles when the number of battles required to beat the game is only 1000. I'm not going to grind 16k battles because the trophy thinks that mindlessly finishing 16000 more battles is completing the game.
I might do one or two more extra things for the platinum or a gold, but overall I usually can't be bothered. Perhaps it's because I play RPGs mostly and in most RPGs the last 40%-60% of trophies are grinding trophies that take anywhere between 50 hours-350 hours half the time.