E-mail will always have a place, due to its asynchronous nature. If I'm not on a daytime schedule, or I'm on the other side of the planet, e-mail will get the message to my recipient, and their response to me. Not to mention those times you just don't want to be interrupted by IM or texting.
I have pretty much solved the issue of POP and multiple computers by setting my mail client (Apple's Mail) to leave the messages on the server for at least a week. In that time, all my computers will have gotten all the messages. An automatic BCC to self, with a filter to file them in the Sent folder, takes care of the rest of the problem.
The biggest problem with both IMAP and Web mail was illustrated in a "Dilbert" strip a few weeks ago. Dilbert is being plagued by Mordac, the Preventer of Information Technology, because he was over quota on his e-mail disk usage. Anything server based suffers the whims of the server management. Using POP mail, I am limited only by my disk space. I cannot tell you how often having an very old e-mail saved the day for me. On a server based system, I might have had to delete the message in question because of disk limits.
As for spam, I honestly cannot say when was the last time I got any. Care in giving out e-mail addresses, and not using spam magnet domains (like AOL or Hotmail) goes a long way in thwarting spammers. Though I realize some folks, like the author, have a genuine need to advertise their e-mail address. For them, I have no suggestions, only sympathy.