Sadly I'd imagine not all that many since so many multiplayer console games can't operate without their servers and they seem to get taken down very fast when the game loses popularity. In addition, many single-player games seem to have some online features too which won't work long into the future. On top of that, who knows how long the digital downloads will be available for and the DLC bought via. the store as well as the PSN/Xbox Live Account authentication.
"Current" modern consoles are definitely going to be more of a pain in 10-20 years assuming the hardware even still works by that point than those a couple of generations before...
From purely a gameplay standpoint, I think JRPGs and other types of offline RPGs will probably be the most-played. Other types of games seem to rely on online/multiplayer components much more.
I definitely think the PS3/360 will hold up better than the PS4/Xbox One as "retro" gaming systems in future. Hardware failures aside, the PS3/360 (More so the PS3) rely on online features much less than the current generation systems, especially with the earlier PS3 games some of which offer no network connectivity at all.