Most of 'em. Only Sith Warriors/Jedi Knights do most of their damage up close. Everything else is all force powers, blasters, etc.
This developer's blog illustrates the 8 different classes, each of which have two advanced classes (or specs, if you will) that explain their role in a group. And of course the site has some descriptions on what all the
classes can do and how they operate.
Sith Warriors/Jedi Knights use lightsabers primary, dabbling a little in force powers but mostly sticking to melee combat.
Jedi Consulars/Sit Inquisitors use some lightsabers but mostly stick to heavy use of force powers. These have the options to either tank or heal, depending on the spec/advance class.
Smugglers/Imperial Agents use blaster pistols and other gadgets/grenades, as well as utilize stealth and cover in order to deal their damage.
Finally, Troopers/Bounty Hunters use blaster rifles and other heavier artillery and other devices.