Gmail
I have Yahoo and Hot mail auto-synced with GMail. I can then either look at each individual folder that houses Yahoo and Hot mail, or simple look at "All Mail" and view all my email at once, with a nice little tag next to each email telling me if it is from Gmail, Yahoo or Hot mail. The key is setting all your Google stuff up on a PC or Mac. Docs, Calendar, Mail, Wallet, etc all have their main settings there, not in the mobile apps.
First pic, is like iOS in that it shows your normal inbox, sent, drafts, etc, then at the bottom, show All labels. Next, you get screen 2 and as you can see you have the Inbox, the Priority Inbox (you know it as VIP Inbox on iOS - Apple loves stealing ideas from Android) and at the bottom you see "All Mail" last screen shows the Orange tab indicating my Yahoo inbox, if I just want to see those emails. Or you can just auto forward yahoo and hot mail from inside those programs into GMail. Entirely up to you. Google apps are very robust.