I've caught up on like 30 something live-action shows since I started watching TV more avidly by around 2008. Of them, about half are ongoing shows, which air at various points during the year.The best way with those is to watch a few per day and not try to rush things. You will eventually catch up.
And this doesn't include anime (of which I've seen a couple of dozen shows and movies thus far).
It's certainly doable, if you allow TV to consume a substantial chunk of your free time.