Nintendo's$60 mini- only comes with 30 games, with no official way to add more.
Emphasis on the word "official," because hackers in Japan and Russia have found a way to add more games -- though it's not strictly legal.
Here's a video showing an NES Classic with nearly 60 games loaded into its onboard storage, including missing fan favorites like Battletoads, River City Ransom and the original Mega Man.
The hack apparently doesn't even require a screwdriver. According to a guide by Russian modder madmonkey (via Ars Technica), all you need is a Micro-USB cable, a PC, a high tolerance for the possibility of malware and a willful disregard for the law -- because transferring your games this way isn't legal, even if you own the original cartridges. (Open-source games designed for the NES may be a different story.)
That said, the hack is proof that Nintendo's NES Classic Edition/Mini is more capable than we originally thought. Don't be surprised if the company releases followup versions with different game libraries at some point in the future.