Yes, there's nothing (in the rules, anyway) preventing multiple Eldritch Knights from bonding with a single weapon.
Once you have bonded a weapon to yourself, you can’t be disarmed of that weapon unless you are incapacitated. If it is on the same plane of existence, you can summon that weapon as a bonus action on your turn, causing it to teleport instantly to your hand.
You can have up to two bonded weapons, but can summon only one at a time with your bonus action. If you attempt to bond with a third weapon, you must break the bond with one of the other two.
However, if the weapon is a magic weapon that requires attunement, only one person can be attuned to it.
As for breaking someone else's bond with a weapon, this is probably only possible with a well-worded Wish. Dispel Magic is the go-to spell for getting rid of annoying magic, but it only works on ongoing spells, which the bond clearly isn't:
At 3rd level, you learn a ritual that creates a magical bond between yourself and one weapon. You perform the ritual over the course of 1 hour, which can be done during a short rest. The weapon must be within your reach throughout the ritual, at the conclusion of which you touch the weapon and forge the bond.
Similarly, the bond isn't a curse, so Remove Curse won't help. You can render the bond useless by being on a different plane of existence to the Eldritch Knight, or being in an Antimagic Field. On the bright side, depending on how your DM interprets the phrase "you can't be disarmed of that weapon", it might be impossible for the other Eldritch Knight to summon it while you're holding it.
The co-operating knights can take turns to use it, but again, depending on how your DM interprets the phrase "you can't be disarmed of that weapon", they might need to drop it at the end of their turns so that it can be summoned by the other knight. Even if they don't have to do this, they're still going to have problems making opportunity attacks, since only one of them will actually be holding a weapon at any given time.
By strict RAW, no. Allowing it wouldn't harm your game meaningfully, however.
Shields are in the armour category, and are thus not weapons. You could easily argue that you could use it as an improvised weapon, but that does not make it an actual weapon. Using improvised weapons as justification for doing this does not hold up, as that would allow you to weapon bond to anything you could feasibly swing around. Including a goblin, if you're strong enough.
The biggest impact allowing this would have on your game, however, is the fact that putting on a shield normally takes an action, while allowing weapon bond allows you to do the same as a bonus action. This is not a massive benefit, and many DMs would allow you to have the shield in hand at the start of combat anyway.
Furthermore, Weapon Bond is what is referred to by the game designers as a "ribbon" ability. Ribbons are abilities that, while flavourful, don't have a tangible effect on game balance.
In short, by a strict reading of RAW, it's not allowed. However, I have not come across a single DM so far that wouldn't allow an Eldritch Knight to weapon bond to his shield, and it will not break your game balance.
Best Answer
Rules as intended, No. It has to be an actual weapon.
Jeremy Crawford sent out a his unofficial ruling on this one over twitter:
He later clarified on this exact topic, saying: