Some may allow you to leave mail on the server only in small amounts or only for a few days. In the future, mail programs and servers may inform you whether or not they support leaving mail on the server. Today, the best thing to do is ask the manager of the mail server or try it yourself. If you check mail from a second computer and don't get the same messages you got at the first, your server probably deletes the messages after you download them. If this happens be sure to use only one computer to check mail or you will have some messages on one computer and some on another.
Some servers are much slower when they have to process a lot of mail.
You will notice that it takes a lot longer for your mail program to log in to the server with these servers. Even with servers that don't slow down in this way, it will take a little longer to check your mail because the mail program has to transfer more message identifiers to find out which messages need to be downloaded. The second slow down usually isn't as noticeable. That will guarantee you get all the messages at all computers. As mentioned above, leaving mail on the server can slow things down.