While I admire guys like toots who can memorize literally hundreds of songs, I am a believer of the Albert Einstein quote "I never commit to memory anything that can easily be looked up in a book." Only so many brain cells survived my youth and I care to use them for more important purposes.
Many musicians use a song book - most pros actually use a teleprompter. You think those stage monitors are all speakers? think again. Look to Elton's right from about :25 to :35 on the below vid. Yup, a teleprompter (and even I could sing most of Elton's tunes by heart). If it's good enough for Sir Elton, it's good enough for me.
Sure enough! Looks like a teleprompter! Thanks for that link too. I have always thought Taupin and John were some of the best songwriters ever and that song is one of my all time favorites.
Some songs I can remember some I cannot. I can remember all of the Pink Floyd songs I have learned but have issues with songs by some other artists. Two songs, "Feel Like Making Love" by Bad Company and "The Man Who Sold The World" by David Bowie and masterfully (IMO) covered by Nirvana, I learned in minutes and had them memorized in the same amount of time.
One thing I like about having songs memorized is that you can adjust how you play them to fit the way you feel they should sound.