I want to get into classic games that I can improve over time and play people worldwide. So far I have chess, go, black jack, scrabble, backgammon. Does anyone have any other game recommendations or specific iPhone / web apps they like? So many of them are ad riddled / privacy issues.
If you're wanting to actually improve over time, you'll have to drop a few. There's not enough time in the day to be a master of all trades. I'd suggest spending more time on Chess - Do a small learning component where you read a book or do some opening theory, then do a portion doing puzzles to learn tactics and spotting common positions in Chess games, then finally play some 10 minute games to put into action what you have practiced.
Card games like spades,hearts or Gin Rummy have solid mobile versions and decent privacy.For classic arcade vibes,Tetris and pac-man still have active global leaderboards.
lichess.org's mobile version is great, you get the "play people worldwide" as well as puzzles and lessons etc, as well as the "improve over time" aspect.