For an indepth discussion check the Does Jehovah require an Organization? article on jwfacts.com.
I try to put here some of the arguments from the Reasoning from the Scriptures book, and some of my own inane comments. I don't have the book in english, so no direct quotes now.
First the definition mentions: 'Jehovah's baptized witnesses don't join Jehovah's organization because of their birth or coercion." JWs imply that in other religion people are "born-in". I found that not true - although I was baptized as a child in a protestant church, I was never considered member of the organization until age 18, by my consent. JWs on the other hand baptize children even below age 10, and that automatically means joining the organization too.
The Reasoning book gives these proofs as to God has to have a human organization:
The angels are organized - Daniel 7:9,10 , Psalm 103:20,21 - no comments here, obviously the angels are organized in a very different way, for example I doubt they give in time slips.
God always gave instructions to his people in an organized way - here it talks about Moses leading the people out, the israelites and the priesthood, then He gave instructions through Jesus, and after that there were elders and was a first century Governing Body; for this last part the verses Acts 14:23 , 16:4,5 , Gal 2:7-10 are given. This is a very important part of their reasoning. But it neglects the fact, that even though an organization was always necessary (anarchy often just won't cut it), God only used the organization, it was not an integral part of His plan. This is why we can find a huge number of occasions when people went against the instructions given from the organizations that was supposed to be God's own, and they were blessed by God. The Hebrew scriptures are chok full of instances when the organization went corrupt and individuals were trying to put things right, because they knew God doesn't like it the way it is right then. After converting to christianism the apostle Paul didn't wait for orders from the organization, but went on to preach, and even later when he visited Jerusalem, he didn't went to the group that the JWs call "first century Governing Body": Galatians 1:17-19
The creation around us proves that Jehovah is an organized God - yep, so He must know the eternal human rule: "Power corrupts; absolute power corrupts absolutely". He sure didn't make a mistake to actually put men to lead other men - like blind leading the blind.
The Bible implies that the true christians will be organized Matthew 24:14, 28:19,20 - how can one preach the good news without organization? Well, like Paul did, as I quoted earlier. Hebrews 10:24,25 - where to lead others, if there's no organization? Well, how about doing literaly what that scripture tells us, instead of trying to force an organization into it? That scripture doesn't tell me anything of a need for an organization.