I have seen One Punch Man, really good stuff. I will check out Boku no Hero.
recently for action I saw, Darker than Black: Kuro no Keiyakusha , I've been given links to one that's currently airing in Japan called Re:ZERO -Starting Life in Another World. That's really good, amazing show so far. Fantasy, action, thriller. You'll have to get onto it when you can.,
Another older one was Blast of Tempest , Saint Seiya: The Lost Canvas and KILL la KILL. Both of those are pretty good and underrated IMO. Far from the classics of course but I thought they're worth it.
They would be the main action ones. Not reading any manga currently which is a sin I know but, cash flow is just non-existent right now.