Any list that doesn't have Barry in the top 3 is wrong by default.
HBO's golden age (the 2000's) wants a word with you.
Regular series:
1. The Wire
2. The Sopranos
3. Deadwood
Those 3 are the greatest and can switch up depending on mood. I will say The Wire is truly the best in terms of quality (the writing A+), but I enjoy rewatching Deadwood and The Sopranos more.
4 and 5? That is way too hard. Rome, Six Feet Under, The Leftovers, and yes even Barry deserves a seat at the table.
Most underrated and underwatched HBO series?
1. Carnivale
2.Treme.
Best HBO mini series?
1. Band of Brothers
2.. Chernobyl
3. Generation Kill
I guess you could even break it down between comedy and drama. That said it is amazing how many HBO shows I am not even mentioning that were great.