A 128-bit security margin is considered good enough currently; a 62-character alphabet (26 lowercase, 26 uppercase, 10 digits) provides 5.95 potential bits of entropy per character; thus a 21.50-character password would provide 128 bits. You can't have a fractional character, so … 22 characters.

Typing 'tgcSq08O2fEZ5hcZk3Gvgk' in from a screen is easy enough, although not something I'd want to do every day.

Though I think 100 random characters is well beyond the point where you're no longer significantly increasing security by adding more characters. You can easily get 130+ bits of entropy with only 20 characters, and even for a ridiculously weak hashing algorithm like MD4 that'd be enough to withstand the entire combined strength of the Bitcoin mining network attacking your password for well over a billion years.