Most lenses are spherical, but...
Are there elliptical, parabolic or hyperbolic microscope lenses?
(I asked a similar question, about telescopes, on Astronomy S.E.; I hope this is not considered 'double-posting').
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Yes, there are lenses of many types for different applications. In particular there a lenses which a specifically called aspherical lenses. These can be used to reduce certain types of optical aberrations, such as spherical aberration which arises specifically because spherical isnt't the best shape for lenses.
There are also lenses which aren't even radially symmetrical such as cylindrical lenses which can be used to adjust a beam of image in one transverse axis but not the other.
In my answer to your related but different question in Astronomy SE I mention that it's so much easier to make spherical surfaces than aspherical that one only uses at most an occasional aspherical surface, and only when it solves a problem that an additional spherical surface can't for some reason.
Reasons that adding more spherical surfaces is unattractive include
The only routine uses of aspherical surfaces in microscope lenses that I'm aware of are