The use of on-line family trees has certainly been a contentious issue for a long period of time. I have heard many people express the opinion that these on-line trees should be avoided completely as they are filled with erroneous information. Unfortunately that can often be true.
Too often, I have encountered well meaning individuals who proclaim a relationship to royalty or persons of historic significance because they found the information on the Internet, the inference being that if it's posted on the Internet is must be valid and correct. This is similar to the argument that an elder family member 'once upon a time' researched the family and told them they were related to royalty or persons of historic significance and therefore it is true.
From my experience, it is absolutely true that on-line family trees can be suspect and error filled. I have maintained a posted public family tree on the Ancestry site for several years. It is absolutely not perfect and sadly not everything in my posted tree is correct and not all facts have sources. Some would advise me that I should therefore not post the tree. I disagree.
My posted family tree is what I consider the other posted family trees to be - a work in progress. For instance, there was a time in my research life when I saw no need to cite my sources when, after all, I had downloaded and filed a digital image on my computer pertaining to a life event or fact in an ancestor's life. As my research continued and I found more and more ancestors and acquired more and more documentation, I discovered that I couldn't possibly remember which document verifying a fact was stored in which file nor could I keep track of matching the documentation to the ancestral life events. So, for some time I have been very busy 'backtracking' and recording source citations in my genealogy database. I know of many reputable genealogists who fall into this same category. I currently have just over 12,000 individuals in my database so there is a lot of work ahead for me to prune my tree and cite my sources.
This is where I see the benefit to me of on-line family trees. In a number of my family branches, I have been successful at finding other researchers that are researching common ancestors, some with whom I have made solid collaborative contacts. Their trees may also contain errors however they may greatly assist me by pointing to facts that I can research, verify, obtain and cite sources for. I'm experiencing a few direct benefits from these on-line family trees.
One, I am able to gather solid source evidence for the events in the lives of numerous ancestors; two, I am gaining exposure to and experience with the records of previously unfamiliar jurisdictions; three, my skills with properly citing sources has greatly improved; and four, my database has become richer and more meaningful as a family history. This has allowed me to periodically replace my on-line family tree with a version that will be more helpful to family members with whom I am collaborating as well as for family members with whom I make new connections.
My family tree has many branches and I owe a debt to those family members, however distant from me, who are pointing me in the right direction to do my own research on a branch where I can find records, verify facts and cite good sources. My advice - use the on-line family trees that you find but also use common sense and be slow to accept what you find as true until you have the facts verified and sourced.