Looking for good Master Theorem examples
A famous example is Strassen's matrix multiplication algorithm, whose running time satisfies the recurrence $T(n) = 7T(n/2) + O(n^2)$. A similar example is Karatsuba's algorithm for fast integer multiplication, whose running time satisfies the recurrence $T(n) = 3T(n/2) + O(n)$. Other algorithms for multiplying matrices or integers supply even more examples of this sort.
The running time of the median-of-medians linear time selection algorithm satisfies the recurrence $T(n) = T(0.2n) + T(0.7n) + O(n)$, which might be too challenging to analyze.
FFT is a classical example of an extremely useful divide-and-conquer algorithm, whose running time satisfies the recurrence $T(n) = 2T(n/2) + O(n)$.