I am here in the U.S. illegally and have never been deported. My spouse is a U.S. citizen/U.S. resident. Can I adjust my status in the U.S.?

Partially.  After I-130 (Family petition) is granted, apply for I-601A, and after approval go to your country’s consulate for an interview.  Then after approval, come back to the U.S. and apply for U.S. residency (I-485) in the U.S.