Conceptually simple linear-time suffix tree constructions
I'm not sure if there were any new results directly simplifying the construction of suffix trees. However, there has been at least one result giving a very simple algorithm for constructing suffix arrays in linear time.

Note that there's more than a conceptual equivalence between these two data structures, since you can use a suffix array (with $\cal{O}(1)$ time for querying the longest common prefix) to build an equivalent suffix tree. This should be a relatively simple exercise, but I can give more details if required.

Also, for practical purposes it's even easier to build suffix arrays in $\cal{O}(n \lg n)$ time, but I guess I'm going slightly off-topic here.