If you're looking for specific games designed for two,
here is an excellent list. I'd particularly recommend
Scarlet Heroes, as a traditional D&D experience designed specifically for one player and one GM, with a number of cool rules hacks to suit that style of play. The author, Kevin Crawford, also released a free rules supplement to add the Scarlet Heroes 1-on-1 rules to Stars Without Number, if you prefer Sci-Fi.
I'd also agree with the comment that most games, even if they're not
designed for two, will
work with two. Some will require some degree of hacking, particularly around social mechanics (Dungeon World's Bonds become tricky when you don't have two PCs, for instance), but you can make them work, usually.
Cypher/Numenera works
tremendously with one PC. One small hack though, to my previous point, is thinking about how XP works. As written, the GM is handing out 2 XP for an intrusion--a huge bonus if the PC has no one to pass that second XP to. So, I'd suggest either limiting it to 1 XP per intrusion, or giving 1 XP and a boon (almost like saying "you get 2 XP but must spend one right now") instead.
Some other games off the top of my head that work well: Fantasy Flight Star Wars; D&D 5E (surprisingly well, in fact--the encounter balance tools allow you to specifically tailor an encounter to one PC); any of the GUMSHOE games (The Esoterrorists, Fear Itself, Trail of Cthulhu, etc.); World of Darkness games.