Trifluoroethanol as a solvent dramatically accelerates epoxide opening with amines and also conjugate addition of amines to enones and acrylates. Thermal Diels-Alder is another good reaction to try in TFE.
1-methoxy-2-propanol behaves as a higher-boiling version of iPrOH. It has a reasonable volatility and it is miscible with water (so it could be pulled off on a rotovap – but also drowned if needed). It has no apparent toxicity issues (unlike methoxyethanol) . This obscure solvent was introduced as an eco-friendly paint thinner but it turns out to be quite useful for direct non-catalyzed SNAr of halogenated heteroaromatics with amines, a reaction that benefits from protic media but where the solvolysis poses a problem. I also used this solvent for high-temp cyclizations done in a microwave reactor.
tert-BuOMe: I suppose the minty reek turns people off but MTBE is a great ether replacement in column chromatography, salt precipitation and recrystallizations. Ortho-litiations have sometimes improved regioselectivity in MTBE, and since this solvent is more resistant to cleavage by organolithiums, it is recommended for room-temperature lithiations with BuLi. MTBE typically does not have radical scavenger stabilizers and the formation of peroxides is negligible – so when you are running a high dilution experiment or evaporating a large volume of fractions from column that contain only miligram quantities of your desired material, MTBE is a good solvent choice.
Acetonitrile: Some people use MeCN only for reverse phase HPLC and it is a pity – MeCN is a wonderful solvent for silylations, acylations, alkylations. Straight acetonitrile is also a pretty good solvent for re-crystallizing very lipophilic compounds.
Benzene is rather useful for recrystallizing stuff, especially with cyclohexane as an anti-solvent. (Benzene+cyclohexane mixtures have a nearly constant boiling point and do not freeze in the fridge). I have seen many examples where a compound could be successfully re-crystallized only from benzene – maybe this has to do with an empiric fact that benzene frequently co-crystallizes with compounds (so in such cases the solvate formation changes the properties of the crystal structure).
Methanesulfonic acid: Old-fashioned cyclizations (Skraup, Isatin, Fisher Indole etc) are typically performed in neat concentrated sulfuric acid. Replacing sulfuric acid with MeSO3H frequently improves the purity and yield. The quench is also less exothermic with methanesulfonic acid.