Actually, Landmarkism is the Baptist form of Campbellism; it developed parallel with, at the same time as, and as a reaction to the Campbellite (Church of Christ) movement, which claimed to have the only real baptism in the only true church.
Let me start by saying I am not a landmarker, but I know plenty of them. One thing I can say with true appreciation is that I have never met a liberal landmarker. They are orthodox to the faith once delivered.
The founders of Old Landmarkism were men such as J.M. Pendleton and J.R. Graves, along with many others. These men were conservative, orthodox, Bible-believing Baptists.
Landmarkism's distinctive doctrines are:
1. There is no church except local churches.
2. There is a true succession of churches from the beginning of the first church at Jerusalem on up through today.(Gunther misunderstands, this is not apostolic, through men, as the Catholics, but through congregations, local assemblies). Some landmarkers believe this can be traced from church to church, all the way back, others accept it as a concept which cannot be definitively proven.
3. Only baptistic churches have this true succession, whatever their name might be.
4. Baptist churches should not accept the baptism of non-baptistic churches, even if that baptism was by immersion. (the doctrine of Alien Immersion).
5. In the Lord's supper, only members of the local church should partake (closed communion).
6. Some Landmarkers also believe in the so-called "Baptist Bride" theory, that the Bride of Christ is the Baptist churches, and other believers are invited to the marriage of the Lamb, but only as guests. Most Landmarkers don't believe this, by the way.
"J.R. Graves" (not the original, but an internet handle), and R. Charles Blair, both on this board, can probably add or correct to this post, and are welcome to do so.