I do not multibox at the moment, as my second account is currently alpha. I have two utility alts on both my main and my secondary account, my main character on the first account and a char especially trained to work in tandem with the first one on the second account. What I most enjoyed about multiboxing so far, is having a scout when traveling or hauling and being able to avoid asking corpmates or friends to help me with tedious work.
In PvP situations, the second char is useful as backpack links, scout, cloaked hauler or fast reship, but overall I would say it takes a lot of training to be able to fly two or more ships well and consistently. I think every player that is good enough to fly more than one ship in serious PvP should be allowed to do so, as it takes a lot of training and dedication and brings no serious disadvantage to their targets that could not be brought in by calling friends.
In PvE, multiboxing is certainly a big question. Multiboxing Ishtars in 0.0, frigates in abyss and Algoses in FW plexes is very common. In my opinion it is good and every players own choice as long as they use it to farm rapidly renewable sites. I see no problem in multiboxing Abyss or missions, and I cannot say how it applies to nullsec. What I do know, is that it is very unpleasant to encounter Algos or Coercer fleets in factional warfare sites. They destroy the market, run sites that were supposed to be ran by small fleets and even attack friendly targets. The drone assist and sometimes even illegal input broadcast programs allow them to be highly efficient in PvP and there is little means of taking them down. So far I do not have any idea on how to remove this problem without causing other players to loose important abilities such as drone assist against kiters or training newbies in high-payout sites.
I am not a miner, but I am not sure I could afford the ships I like to fly if there were no multiboxing miners. At least in highsec, it seems like the high respawn rate of the asteroids allow them to consistently gain their income and keep the industry and markets stocked without causing harm to others.
All in all is multiboxing no way to replace space friends. It can be useful in many situations, but in the end a good friend is worth more than an alt. Alts do not listen to you, they don't laugh with you when you fly a silly fit, they don't suffer with you over a lost ship. The friendships made in Eve can be stronger than current allegiance, in the end, the game is not about pixels, ISK or even spaceships, it is about the people you meet on your way. Of course hardcore solo players will not conquer with this and everyone can play as they like, but in my opinion, Eve is about people, not places.
(btw, I want my people&places tab back, I miss having everything in one window :p )