This is a really hard subject to give one definite answer on. There are so many games I've played over the years that I have enjoyed.
For the most nostalgic and fun in general, the award goes to Halo 3. I remember way back when when we all played it, YouTube was full of unregistered hypercam and Dreamscape and Paralyzer songs, and let's not forget Breaking Benjamin's Blow Me Away from Halo 2. I had lots of fun playing, particularly in the Forge mode, where I would go into something like Foundry and go deleting everything on the map and then making whatever crazy stuff I felt like making. Yes, there was a time when you had to go around and delete every single piece of the map that you could find while watching your "budget". We actually have had a lot of the Halo games, including CE (on both PC and xbox), 2 (the limited collectors edition in that super cool box, this was a game we spent a LOT of time playing in xbox live back in the day), 3, ODST, Wars, Reach (the collectors edition), Master Chief Collection, 4, 5, the list probably goes on.
Besides the halo games, more recently I've been having quite a lot of fun with sandbox titles like Blockland and Garry's Mod. I like these lots-of-games-in-one kind of games, and much of my time has been spent recently playing these games due to their "unlimited" replay value and their gamemods and communities. I also had quite a lot of fun with games like ROBLOX and Wizard101 back in the day, although I don't play Wizard101 really at all anymore (I still have my account, surprisingly) and while I do occasionally play ROBLOX, I don't play it as much due to the cancer community and the like. Minecraft is also a pretty good sandbox/survival game that I had a lot of fun in after I was introduced to it by my older brother around Beta 1.3. I still like to play Minecraft quite a lot, mainly with modded servers hosted by Blockland forumers, as I like modded servers for how they let you do many more things than the vanilla game. Heck, I even host my own modpacks.
I've also enjoyed more recent shooter games like Splatoon and Overwatch, which are both really darn good games. I haven't really been playing splatoon as I grew bored of it (and now there are no more splatfest events occuring in the game to spice things up), and I play overwatch occasionally.
There are probably many more games that I'm leaving out here, but I don't want to continue this giant wall of text.
TL;DR I don't have one specific favorite video game, but I sure do have some favorite games.
EDIT:
KILL ME
