Are movies recorded on film?
Yes, many big budget features are "still" shot all or partially on film. 
Here's a list of a number of movies shot on film for 2014:

Reasons vary, but many consider film to have a particular reality or consider themselves purists and apprecate the sublties they believe analog film can offer. 

Here is an interesting article on why Star Wars: Force Awakens was shot on film rather than digital:
http://petapixel.com/2015/12/16/star-wars-the-force-awakens-was-shot-on-film-and-kodak-may-be-profitable-in-2016/

And here is another:
http://www.techradar.com/us/news/home-cinema/high-definition/why-has-star-wars-turned-its-back-on-digital-film--1310861

IMAX cameras shoot on 70mm film. Since many big budget features end up shown in IMAX they use IMAX cameras for all or usually parts of the film. Certain scenes in Batman V Superman were filmed on IMAX "real film" cameras.
Reference here:
http://batman-news.com/2014/11/13/batman-v-superman-dawn-justice-will-shot-imax/

About IMAX cameras here:
https://en.wikipedia.org/wiki/IMAX