Light Repeating Blaster: An excellent all-around weapon, the benefit of the light repeating blaster lies with its amazing firing rate. But, there are downsides, specifically damage. Try and use the light repeating blaster against tougher enemies (such as destroyer droids or boss creatures), and you'll face a difficult fight. The light repeating blaster fires so fast, it'll usually stop enemy droids in their tracks, helpless as they're continually barraged with bolts. Against the flying droids in the Coruscant level, the light repeating blaster is especially effective.
Heavy Repeating Cannon: On some levels, you'll come across an enemy turret emplacement that you can use. To put it simply: if it can be used, use it.
Flash Grenade/Thermal Detonator/Gungan Energy Ball: While not as powerful as the thermal detonator, the flash grenade can still pack a hefty punch. Against a huddled mass of battledroids, a flash grenade will usually destroy a couple or incapacitate them long enough to blow them apart with your blaster. The Gungan energy ball is a special grenade that immobilizes mechanical units; use it in conjunction with a blaster or the lightsaber to eliminate droids.
Proton Missile Launcher: When you want to clear a room, you can't get much better than the proton missile launcher. Ammo is pretty scarce for this powerful weapon, so use the missile launcher when there are several enemies - or just plain tough enemies - in an area. The missile launcher is especially effective against turret emplacements, as you can destroy it quickly - and from a great distance - before taking significant damage.
Droid Stunner: Queen Amidala's default weapon stuns battledroids, so her guards (and Captain Panaka) can eliminate them easily with blasters. The droid stunner's range is pretty bad, however; to stun a droid, you'll probably take plenty of damage yourself. Locate a better weapon, even a basic blaster rifle, as soon as possible.
Next: The benefits of the Force push