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.
Thai Air has two direct daily flights between Bangkok and Koh Samui.
Direct international destinations from Samui with Bangkok Air are Singapore and Hong Kong on a daily base.
Furthermore also Firefly and Berjaya-Air fly between Kuala Lumpur, Langkawi and Koh Samui.
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.