Playing
lichess.org – arguably the best platform for playing for most users. Free, open-source, funded by donations, with very fast interface and many features.
Tactics training
ChessTempo.com – in my opinion the best platform for tactics training. Basic membership is free, but it is the best with gold membership (only $4 / month). All puzzles are tagged and rated; most of them contain user comments. With gold membership you can even create custom sets of puzzles, i.e. containing only puzzles with certain motive (like fork or mate in 2), puzzles that lie within some rating range, etc.
My chess journey 