You know this big machine thing you only ever use to look at the internet on? Well, here's a thing. It's got more power inside it than is really necessary to just use to F5 your favourite and least favourite internet sources all day. You can play things on it. Proper things from the olden days, too, not rubbish new things that always force you to be part of a war (on a team, too).
Sites like Playr have been successfully skirting the legal issues involving in emulating Nintendo games without all the admins ending up financially ruined and in prison for years, with a massive catalogue of Game Boy and Game Boy Color games available to sample. Given that the Game Boy version of Mortal Kombat is only like to offer 90 seconds of bizarre enjoyment at most, it's ideally suited to populating a browser tab, being laughed at for a minute, then closed.
For PC games, the most capable option for enjoying older titles without worrying about downloading disc images and coping with demands to access servers taken offline in 2005 is by browsing through the gaming archives of Archive.org. The likes of Indiana Jones and the Last Crusade and Wolfenstein 3D can be found up there to play via DOS emulation, or the even easier to navigate search box of Playdosgamesonline reveals stuff like Populous II, Theme Park, Championship Manager 93-94 and... most old PC games that may hold a special place in your mind.
Plus there are obviously thousands of standalone titles designed specifically for the browser. Thousands are also rubbish, but things like the beloved Spelunky aren't. Nor is Unsolicited, from the maker of Papers, Please.
Archive.org doesn't just handle PC emulation. Its Mega Drive section has 574 games listed and playable through a browser. Some are unfortunate titles like Alien Storm and Two Crude Dudes, but there's also Streets of Rage II -- which is literally the last game you might ever need, such is its impeccable 10/10-ness. The site even has 22 titles for the Amstrad GX-4000 to play in a browser, so you should now have more than enough tabs open to swamp your browser and gets the fans whirring at maximum ahead of a full day of remembering things.