Gaming can be expensive (like most things), but it can also be done cheaply (like most things).
If you buy all the current game systems, and buy every AAA title the week it comes out for $60, you can burn through money like it's going out of style. But there are other ways.
You can apply a flat x-year delay, as was mentioned above. You can simply emulate or pirate. I recommend a different approach.
I now look for video games to play the same way I now pick out movies to watch. There are loads of great games/movies out there that I haven't played/watched. Some are recent, some are older. If a game/movie is new and people are talking about it, 90% of the reason they're talking about it is because it's new, regardless of quality. If an older game/movie has notoriety, it's (generally) because of its intrinsic quality or influence on the industry. This way the game/movie is ranked against every other game/movie ever made, not against what else came out this week.
With this mindset at work, often newer games/movies seem like a gamble at best. If I haven't seen The Godfather, what business do I have seeing Fast & Furious 6? If I haven't played Chrono Trigger, what business do I have buying Call of Duty 37? When the choice is either a known "classic", or a maybe good/maybe bad current game/movie, the choice is obvious, even disregarding the cost.
But the cost savings are dramatic.
If my girlfriend and I want to see The Godfather, my cost is either $0 at best (rent DVD from the library), or $13 at worst (buy the fancy Blu-ray disc from Amazon.com). If we want to go see the big new Tom Cruise Runs Around Again film, that's best-case scenario $11 (two discounted tickets), or $26 worst-case (two IMAX tickets).
If I want to play Chrono Trigger, I can buy the cartridge on eBay for $80. I can go to the store and buy the newest PS4 shooter for $60. After I'm finished with Chrono Trigger, I can resell it for what I paid for it, because it's a known classic with a now-constant value. That PS4 shooter probably is worth half of what I paid for it, maybe less. Even with really expensive classic scarce games like Chrono Trigger, you still come out ahead.
An example of how this has worked for me: Over the years (since ~2001), I have been an Nintendo 64 fan. I had bought many of the best games for that system. I sold them all earlier this year on eBay for $295. I went back and figured out that I paid a total of $270 for them over the years. So even after eBay fees and shipping, I about broke even, and I got 13 years of Nintendo 64 fun out of it. And they were all great games. Hard to beat that.
If you only buy good games, they will retain their value. If you buy bad old games, they will only cost a few bucks. If you buy bad new games, they'll probably still be $60 new, but worth only a few bucks within a year.
Since I truly adopted this mindset of looking for movies to watch and video games to play, I've spent very little on either. The last new game I bought was Skyrim (Steam), and I've probably been to the movie theater once or twice in the past year, always as a social outing.
I've also abandoned any idea of a "collection" of either. After I play through Banjo-Kazooie, I don't need to keep the cartridge as some sort of perverse trophy. I can sell it and pass it on to someone else to enjoy, and recoup the space and money. If I really want to play it again in five years, I can track it down again.
And this doesn't mean you can't play dumb-fun "non-classic"/"non-art"/whatever games/movies. But if you really want to watch Fast & Furious 6, you can probably find it in the bargain DVD bin in a year, and I'm sure there will be plenty of copies of Call of Duty 37 for 99 cents at Goodwill in 2018.