Are parsimonious models always better? In my classes there is always some mention of AIC/BIC. Certainly model complexity is an important thing to penalize for in the sense that you don't want to include variables that are unnecessary.
Is there any research into just how much you should penalize complexity, is it ever a good thing? Do domain-specific fields in Genetics or Neuroscience treat model complexity differently, for example?
Have there been really complex models that - counter to our intuition - have been accepted by the academic community? 
 A: Parsimonious models are always preferred over less parsimonious models assuming the normalized objective performance is equivalent. That’s where AIC/BIC comes in, as a way of putting candidate models on the same playing field (since more highly parameterized models perform better). This is consistent across disciplines in theory, but perhaps not always in practice. 

Is there any research into just how much you should penalize complexity, is it ever a good thing? Do domain-specific fields in Genetics or Neuroscience treat model complexity differently, for example?

You should penalize completely based on the number of free parameters, and most would say it’s always a good thing. I can’t speak to genetics but in neuroscience, it’s generally expected that one abide by model selection criteria like AIC/BIC. Any discipline with a strong quantitative component will agree. 

Have there been really complex models that - counter to our intuition - have been accepted by the academic community?

Absolutely, but many of those cases don’t take a model comparison approach. Since you mention neuroscience I’ll go there for an example. The Wichmann & Delong ‘gold standard’ model of Parkinson’s disease can be expressed as a flow chart from pallidus / subthalamatic nucleus to cortex. In whole it is quite complex and while it makes logical sense given known biology, it’s not proven and also generally not pitted against competitor models. But, it remains accepted by the academic community per your question (me included; it’s probably accurate to a first approximation).
