Prominent applications not suited for distributed computing
Most of the old (de)compression algorithms were not suitable for parallel or distributed computing. The variable length nature prevented decompressing later parts of the input stream before decompression of earlier parts was finished. And adaptive dictionaries often prevented compressing later parts of the input stream before compression of earlier parts was finished. Both issues can probably be avoided at reasonable cost, and maybe some modern (de)compression algorithms actually do this.
Nearly all cryptographic hashes will not be suitable for speedup by distributed computing. Any feature which could be exploited to make distributed speedup possible also risks being exploitable to weaken the cryptographic security of the hash.
Many popular black box opimization algorithms are not suitable for distributed computing in their basic form. Especially local optimization algorithms like the Nelder–Mead method or the Broyden–Fletcher–Goldfarb–Shanno algorithm are inherently sequential. But even more global algorithms like simulated annealing are local (and  sequential) in their basic form, even so it is possible to develop parallel forms for them.