Seeing a Batman and Superman thread, I figured it was time for everyone's favorite web-slinger to get his due.
The reason Spidey is so popular has been stated countless times by so many people over the years: he's your everyday man. Despite his great powers, he is not immune to the trials and tribulations of everyday life. He's the original hardluck kid, but he still catches those much needed breaks.
If you want to check the Lee/Ditko, Lee/Romita era books, you can check either the Marvel Masterworks books, Essential Amazing Spider-Man vols., or pick up 40 Years of Amazing Spider-Man, a CD-ROM collection of over 500 ASM comics on 1 disc.
Actually, Spider-Man has had a TON of good runs with various different writers and artists. Those that say Spidey was only good back in '60s-'70s are drinking drano.
Remember, true believers, with great power, comes great responsibility!