I used to use Yahoo! until it became spam city. I used it since the late-90's before closing my account a couple years ago for good.
Now just Gmail. Been using it as my main for the last 7 years or so. Works well with Google Voice which I've been using since 2011. I flashed a ROM to my Android and had to zip Gapps (Google apps). I think my Gmail app is the important Google app to me followed by Play Store. I can live without a YouTube app since I have TubeMate or can stream from the mobile browser. I can live without Google Maps since I downloaded an app called Maps Me for offline apps. And I can live without Chrome since CM Browser is much better.