Equivalents of PubMed in other fields
Unlike PubMed, many of the discipline specific indexing and abstract services tend to be run as proprietary services:


For Engineering there is Engineering Village 
For Chemistry there is the Chemical Abstracts Service (CAS) SciFinder
For Theology and Religious Studies there is Index Theologicus
For Philosophy there is The Philosopher's Index and PhilPapers
For Geology there is GEOBASE and GeoRef
For Economics there is EconLit and RePEc
For Mathematics there is Mathematical Reviews and zbMATH (hattip Dave Renfro)
For Electronics and Computer Science there is IEEE Xplore
For Agriculture there is AGRICOLA and AGRIS


Wikipedia has quite a full list that might be of further interest:
https://en.wikipedia.org/wiki/List_of_academic_databases_and_search_engines