Yes, you can use an established email address with a standard email client like Microsoft Outlook, Mozilla Thunderbird, Apple Mail or even Eudora. This software will receive the incoming mail from the servers to your inbox and allow you to sort and filter by date, subject, etc.
The alert messages from these servers aren't frequent. You should direct them to an email address or (ideally) distribution group that people will actually check regularly.
A typical message from an HP server looks like:
To: <[email protected]>
Subject: HP Insight Management Agents Trap Alarm
Trap-ID=3046
Physical Drive Status Change: Slot 0 Port 1I Box 1 Bay 1.
Status is now Failed.