This question came up when I did my video about Chapter 2 of the new Dungeons and Dragons Fifth Edition Dungeon Master's Guide. Personally I don't think you need to explore any planes besides the plane your game takes place in. That doesn't mean you can't use monsters from those planes. I use monsters from other planes fairly often.
The planes are very interesting and could make for some fun sessions. I do think playing in them could get old really fast though. They are good for a couple sessions I think but for extended periods of time I am not sure how long it could maintain my interest.
These are just my opinions but I want to hear yours. What do you think of the different planes? Have you used them extensively in your campaigns? How were they received by your players?