Mutliplayer is way more fun than playing against the computer. The HARD part is finding games that suits you - and games that don't last too long or are too slow-speeded! It is also hard to find (random) online games where people don't quit after a short while.
Nothing beats the fun of playing Civ IV with dedicated players. However, it actually DO require dedication so this demand a lot of time from players. We try to do it in our leagues, and it is very much fun when it works. However, it takes a lot for players to sign up to the games because of the timezone and length-of-game issues (we normally play 4½ hours with few breaks and at a time most suited more European countries).
PBEM = Play By EMail - which is a slow way of playing where each player gets a mail with a savegame and send it off manually to the next player. A game can easily take months or even years.