Your Youth, in a Browser!
I've mentioned many times before the questionable nature of downloading video game ROMs in order to emulate them on your computer. (Heck, my very first article in Linux Journal was a description on how I built a MAME cabinet!) Although I have some emulation tricks up my sleeve for future issues, here I thought I'd mention the vast number of Flash-based emulators available on the Internet.
Some sites are more ad-laden than others, but many of them work quite well. For example, for old-school Nintendo games, check out https://www.nintendoemulator.com for a huge list of fully functional games. I played Super Mario Brothers on my laptop using Chrome's built-in Flash and wasted a great deal of time doing so!
As with downloading and emulating ROMs locally, you should be aware of potential legal and moral issues. I actually own so many old games that I don't have any moral problem playing with emulators, but I'm not the ultimate authority. If you want to try out some on-line emulators, either search Google for a few options, or visit the site mentioned above. It's a great way to spend a boring afternoon!