I've been using Thunderbird for many years. With that, I copy e-mails I want to keep to separate "mailboxes" and delete most. I can back those mailboxes up to anywhere I choose and remove them from the main setup (although I don't need to remove them).
I can read the backed-up e-mails as a block, or I can copy them back into the Thunderbird directory with a suitable name ("Aviation Jan - Aug 2013" for example) and then read them individually in Thunderbird.
I used Outlook for a while, but the .PST file got corrupted and all my e-mails, address book, and diary became inaccessible. The same glitch corrupted the backup file. Never again!