Personal preference with no single right answer. I've done some extended tours alone including 365 day long tour in 2001 that took me around Australia (8 months), across USA (2 months), New Zealand (1 month), India (1.5 months).
For me there is a continuum on my tours:
- In English, speaking countries and more in the developed world; I like touring alone and freedom it provides.
- Where English is not the primary language, but still reasonable cycling infrastructure; I like touring with others. For example, in crossing Russia in 2007, I cycled with another person I found on Adventure Cycling web site. I've also done trips in Armenia, Indian Himalayas and Ukraine/Russia with my brother. Recently, also had good experience with another cyclist riding through Central America.
- Where logistics seem difficult or more "exotic", I've also done some supported tours. For example, TDA across Africa and through China. Also taken some Spice Roads trips in southeast Asia (some places in southeast Asia not as exotic as I thought).
As others describe, sometimes even if you go solo, you aren't quite "alone" when you are running into other people - often multiple times. For example, never felt much alone in Outback Australia since I was on the primary sealed road. Similarly, riding the US Pacific Coast, one will often encounter other cyclists.