I love this question as it is one I've thought about a few times. I'm not much of a gamer, so my "take" on this question is probably vastly different than a person who loves playing games. For the most part, I think games (especially video games) are an unproductive waste of time. Having said that, I understand that we all need some down time in order to enjoy life. While I prefer to spend my down time doing things that are every bit as unproductive as playing games, I do, nonetheless, play a game from time to time.
My favorite game of all time is Magic: The Gathering. I go through very long periods where I don't play at all (i.e. years), but I still have my card collection and I still get really addicted to it from time to time. I treat all my cards with care so that they will retain as much value as possible should I ever decide to sell my collection. (I keep all my cards in protective sleeves, and I store them away from sunlight.) The game can be very expensive over time because some rares (especially the newer mythic rares) can cost as much as a video game for 1 single card. On the other hand, you can get hours/weeks/months and even years of play out of a $9 pre-constructed deck.
For my time & money, there's no better game.
As far as electronic video games go ... I find it very difficult to get *any* value out of them at all. Video games bore me to tears. I would generally rather read a book, clean the house, surf the web, watch a movie, or do just about any other non-productive thing than play video games.
Having said that, there is one video game that comes to mind that I have gotten tremendous value out of. StarCraft. I bought the SC/Broodwar Battle Chest like 10+ years ago and I think I only paid $29 for it. But in the last 10 years, I have played that game off and on many, many times. In fact, about 2 months ago I got the urge to play it again ... so I got my discs out, installed it, patched it, and played several games for a period of about 5 days. It was great fun ... and I'm probably done with it for another year or two.
But the fact that this game from the late 90's is still working on modern hardware and modern operating systems is a true testament to the value that you can get from some games.