The Airport bus goes to Stockholm, but when I checked their site I see that they again have changed routing:
"Flygbussarna Airport coaches operates to and from Stockholm Skavsta Airport on these routes:
Skavsta - Stockholm Cityterminalen (non stop)
Skavsta - Södertälje - Skärholmen - Västberga - Gullmarsplan (Stockholm)
Skavsta - Norrköping - Linköping
Skavsta - Eskilstuna - Arboga - Örebro"
...so the two buses to Stockholm are no longer one through Skärholmen and one through Gullmarsplan. It's one non stop to CityTerminalen (by T-Centralen and Centralstationen for the trains) - and one that goes through several stations, including Skärholmen, and stops at Gullmarsplan...
http://www.skavsta.se/en/content.asp?area=2&id=62
http://www.flygbussarna.se/Default.aspx?lang=EN
However, if you arrive late you may not afford to be picky - if you not take the next bus, the one for your flight, it may be long before the next.