Door to door evangelism was a tool pioneered by Evangelist D.L. Moody. It was an effective means of contacting people during a time when other door-to-door forms of solicitation were the norm. (i.e. the Fuller Brush Salesman) Russell used it as a way to sell his books and Rutherford made it a requirement to sell his. (If you read the old literature they do not hide the fact that this is a sales activity.)
Despite what the Witnesses claim there is no scriptural prescedent for this type of evangelism. When Jesus sent out twelve disciples as apostles he specifically instructed them not "to be transferring from house to house", rather they were to find an open home in one area and stay there and use it a base to share the message. Per the scriptures, early Christian preaching was done as guests in private homes, in public places (markets, wells, pools), in religous buildings (the Temple, synogogues), and in rented facilities (the Hall of Tyrannus). You never read of Christians going "door to door" systematically in the manner of Jehovah's Witnesses.
The Scriptures that the Witnesses will fall back on is Acts 20:20 where Paul says, "I did not hold back from telling YOU any of the things that were profitable nor from teaching YOU publicly and from house to house."And Acts 5:42 where we read, " And every day in the temple and from house to house they continued without letup teaching and declaring the good news about the Christ, Jesus."
The Greek word for "house to house" can also be rendered "in private homes", which is more to the point of what Paul is saying, claiming he openly shared his message of Jesus, both publicly and privately. It also has the same thought at Acts 5:42 where it highlights that the message of Jesus was shared both publically (In the Temple) and privately (in homes).
It is important to note the NWT does not render this consistantly and uses "in private homes" instead of "from house to house" at Acts 2:46
" And day after day they were in constant attendance at the temple with one accord, and they took their meals in private homes and partook of food with great rejoicing and sincerity of heart"
Ray Franz details that there was a time in the 70's where the Governing Body agreed with this and stopped stressing the "house to house" work accordingly before reverting back to their earlier stance.