Will people still remember and discuss today's popular TV shows 10-20 years from now?

Yes, of course they do! Most of them are still on TV. I grew up in the 80s but I grew up on shows from the 60s (Star Trek, Man from UNCLE, Land of the Giants, Lost in Space) as well as more recent stuff. A lot of my favourite shows started more than 10 years ago and are still going on: Doctor Who, Simpsons, South Park, Red Dwarf, etc. Plus a lot of TV shows have finished but were bloody awesome and I still talk about them whenever I can: Quantum Leap, Firefly, Buffy, Being Human (UK), Monty Python's Flying Circus. Plus there are some amazing shows on right now that are blowing my mind and making big waves in the medium: Orphan Black, True Detective, Grimm, TMNT 2012. I'm always thinking about what TV shows I want to show to my kids. You are really missing out if you don't watch series. Just make sure you choose carefully.

Yes most definitely! Especially considering the people who watch the shows out now will be parents and (hopefully) pass what they saw onto their children. A lot of people in our generation, well for me anyway, grew up watching shows my parents did because of how they enjoyed them when they aired so it only seems natural for this to happen. I can almost guarantee with a certainty that they'll go down in pop culture as well plus the shows that came before these shows out now like I Love Lucy, Star Trek (ALL) and others will be regarded also.

Are you kidding?! Friends aired from 1994-2004. Just look up the number of discussions on it on Quora or anywhere! Its not just friends, there a number of great shows that people still watch and talk about. Take Sienfeld for example.