What MMOs influence Sword Art Online and Log Horizon?
His main inspirations would be

Ultima Online
Ragnarok Online


Reki Kawahara was in the Manga Studies Club. He drew manga and illustrations during his time there. Kawahara would often head to the arcade with his fellow members to play fighting games . He also started playing online games in 1998, starting with Ultima Online. Kawahara also played Ragnarok Online, his most played game (although he stated World of Warcraft during Sakura-Con 2013)
He felt it would be more natural to write about net games.

For some more of his inspirations and why he decided to write you can read a brief biography about him