if you are using online wallets then i think it is no use to remember your bitcoin address as they are using multi address technology which created every new address after we do new transactions , ya but if you are using hardware wallet then i think we can remember it. but nowadays so new technology has come that we can store it and use it any where without remembering it.

It's too long to remember and too many to remember.

I just try to remember the first and last 3 characters.

From my main address I remember the first 4 and last 4 digits.

This is very handy when making payments. Because i double check it this way.

im remember 3 digit of my address but never trying  to memorize details of my address
im use more than 10address maybe 20-30 address  

better i save it in my address book (mycellium) so if i want to send to bittrex i will send to this for huobi this  etc.

I really don't way too long and too many to remember and keep up with.

I do always try to remember the last 3 and first 4

No cause its hard to memorize the bitcoin address haha