I stop short of recommending B-trees as the only tree structure you need to know. I think if it matters at all what kind of tree you're using, you're deep enough in the guts that it pays to know the differences between B-trees and basic trees.

To me, this is especially relevant today, since if you need a "B-tree", you probably need a standard relational database (MySQL/PostgreSQL/SQLite), and if that doesn't work for you, you'd be advised to know what the tradeoffs are with a regular tree. There are scenarios where B-trees are suboptimal.

Cache-obliviousness, which is still new, is also changing how we look at trees, since in one sense a B-tree is a hack on the basic tree structure to exploit locality. Representation matters more today as well. This is a longer conversation. Suffice to say I think this is an area of active and useful research, and wouldn't rule out either class of tree.