Bangkok Air operates direct flights between Samui and; Bangkok - Suvarnabhumi Airport, Chiang Mai (change over in BKK), Krabi, Pattaya, Phuket, Sukhothai (via BKK) and Trat.
Direct international destinations from Samui with Bangkok Air are Singapore and Hong Kong on a daily base.
Other direct bus connections from Koh Samui are to/from Hat Yai, Phuket and Surat Thani town.
Various mini buses go to plenty of other destinations on a daily base from Koh Samui, check with local Samui travel agents for time schedules and prices.
From Koh Samui you can also take a ferry link and bus shuttle to the Surat Thani train station and take a train to the Malaysian border.