The iPhone and iPad are great for quickly handling email. However, if something is important, or requires a lengthy reply, or you can only get to it later, or you simply want to keep your inbox close to zero, the iPhone and iPad are also great for quickly sorting and filing your mail into well organized mailboxes.
It's worth noting that some account types allow for folder mapping which means you can move messages from one account to a different account. When moving a message you can go back to the account list and choose a different account. If your email service provider doesn't support this, you'll just receive an error message stating the messages can't be moved.