GMail using the GMail Pop3 fetcher feature.
I decided so, because I think that too many points to check was a very losing time strategy.
I've also more than three mobile devices (iPhone, Android tablet, two Android smartphones and so on), and each device was configured to check all mail accounts wasting energy and data plan.
Initially I was looking for a way to migrate all my sent mail (thousands of mails) to my GMail account.
Unfortunately there is no way to do it with a pop3 access (at least I haven't found a way).
But if you have an IMAP access to your mail account, I suggest you to manually move all your sent mail to "Sent" folder (label) of the GMail account using a standard mail client (like Mozilla Thunderbird, Microsoft Outlook or others).
Once moved all sent mail, you can move all your received messages on GMail Inbox folder. Of course, you do not need to manually move your received messages if your mail account was configured to leave messages on server.
When all this is done, you can access your GMail account using a web browser and go under Settings -> Import and accounts and configure the section "Check mail from other accounts" with the required parameters to access to your external mail account.
If you want to send messages from external mail account, you can configure the "Send message as" section.
Now I've all my mail accounts (over 20 thousands of mail) centralized on GMail and all is going good.
I'm saving time and money!
Thank you Google!