What's the opposite of "embarrassingly parallel"?

Inherently sequential.

Example: The number of women will not reduce the length of pregnancy.

There's more than one opposite of an "embarrassingly parallel" problem.

Perfectly sequential

One opposite is a non-parallelizable problem, that is, a problem for which no speedup may be achieved by utilizing more than one processor. Several suggestions were already posted, but I'd propose yet another name: a perfectly sequential problem.

Examples: I/O-bound problems, "calculate f^1000000(x₀)" type of problems, calculating certain cryptographic hash functions.

Communication-intensive

Another opposite is a parallelizable problem which requires a lot of parallel communication (a communication-intensive problem). An implementation of such a problem will scale properly only on a supercomputer with high-bandwidth, low-latency interconnect. Contrast this with embarrassingly parallel problems, implementations of which run efficiently even on systems with very poor interconnect (e.g. farms).

Notable example of a communication-intensive problem: solving A x = b where A is a large, dense matrix. As a matter of fact, an implementation of the problem is used to compile the TOP500 ranking. It's a good benchmark, as it emphasizes both the computational power of individual CPUs and the quality of interconnect (due to intensity of communication).

In more practical terms, any mathematical model which solves a system of partial differential equations on a regular grid using discrete time stepping (think: weather forecasting, in silico crash tests), is parallelizable by domain decomposition. That means, each CPU takes care of a part of the grid, and at the end of each time step the CPUs exchange their results on region boundaries with "neighbour" CPUs. These exchanges render this class of problems communication-intensive.

Im having a hard time to not post this... cause I know it don't add anything to the discussion.. but for all southpark fans out there

"Super serial!"