User blog comment:Hunter89/Will be continued?/@comment-6697950-20131125171405

Currently, a special recap episode, called the Extra Edition (linked to an article on this wiki about it with an outline of the plot) is set to air on 31st of December/1st of January (the episode will also be streamed via Crunchroll and some other site to other countries). This is probably why some sites list the anime as "ongoing", though I wouldn't call this one a movie, as, from the plot, it's pretty much a definite that it is going to be just a swimsuit episode with recap elements. A lot of people speculate that the episode's main purpose is to announce a 2nd season (first 25 episodes are just 1 season that consists of 2 story arcs, but it's still the same season) and that is currently our best chance for such on announcement. Quite a few people think that the last sentence of the outline that says that "Kirito comes in contact with someone..." hints an upcoming announcement (people guess that the "someone" might be Kikuoka Seijirou who will introduce the plot of the next arc)

Anyway, there isn't anything official about a 2nd season yet, just speculation among the fans. Though if the anime studio wanted to continue, they'd likely have enough material for at least 2-3 more seasons, or 1 movie and 1-2 seasons, as the original book has 2 more main arcs that the anime hasn't touched yet, while the 4th arc is twice as big as the first three combined.