Setting up Gmail or Hotmail through the preset "Add Account" dialog isn't good enough, because it can't immediately push new messages to the phone. Instead, you can set up these in-boxes through Microsoft Exchange, so new emails get pushed right to your iPhone. To get started, go to Settings > Mail, Contacts, Calendars > Add Account... and select Microsoft Exchange. On the next page, enter your full e-mail address, password and whatever inbox name you'd like, then hit "Next." More options will appear. Enter "m.google.com" or "m.hotmail.com" in the Server field, leave the Domain field blank, enter your full e-mail address in the Username field, and your password in the Password field. Hit "Next," and on the next page, deselect Contacts and Calendars unless you want to overwrite your phone's existing contacts and calendar. Hit "Save," and you're good to go.