For me the most interesting is Return of the King. This part is about my hero Aragorn and we've in this part the most effective and the biggest battles!

For me its when Frodo is leaving the Shire with Sam Merry and Pippin .. they are just amazing together haha

Two Towers. This explains it all, one of the best scenes in the movies: https://www.youtube.com/watch?v=FnYbsAVdkYw

Whaaat you can't have just ONE best part of The Lord of the Rings! Any part with Viggo Mortensen is the best to be sure, but I would have to choose either the epic ride of the Rohirrim to Gondor's aid or the battle at the Black Gate with Aragorn's rush and all :)

the best scene is (in my opinion) gandalfs fight with the balrog of moria and his return.

but the best movie over all is part 3 i think

The best part for me is the Battle of the Pelennor Fields. In one moment it looks like hopeless battle until King Theoden comes with his army of Rohirrims and wipe the orcs out.