You never said what type of bike you had so I'll guess and say you have a crusier. If so, I would check your rear sprocket. Sometimes they don't fit well over the dust cap on the hub and when you tighten down the bolts, it locks the wheel up. Also, check your brake arm and make sure it isn't hitting the bolts holding the sprocket on. You might have to bend it to get some clearance.
If it's not those things, it must be your clutch. Check these things out and report back if you still need help.
Edit: I just thought of this, if you mean that it feels like there is a constant drag on the rear wheel, that is the clutch system. It will always have some drag to it.