trending

You can use trending method. E.g.:

https://api.themoviedb.org/3/trending/movie/week?api_key=###

popular

You can use discover method with "&sort_by=popularity.desc". E.g.:

https://api.themoviedb.org/3/discover/movie?api_key=###&language=en-US&sort_by=popularity.desc&include_adult=false&include_video=false&page=1&with_original_language=en

top_played

We don't collect this information, but maybe you can sort discover results by number of user votes to get similar results:

https://api.themoviedb.org/3/discover/movie?api_key=###&language=en-US&sort_by=vote_count.desc&include_adult=false&include_video=false&page=1&with_original_language=en

top_collected

We don't provide this information.

top_watched

We don't collect this information, but same as top_played, you can sort discover results by number of user votes to get similar results.

recently_updated

You can use changes method to get changed movie/tv/person IDs.