Go into options->video settings and you can see Render Distance and Max Framerate.
Your monitor is most probably going to have a refresh of 60 or 75, meaning that such number is the max FPS it can actually display.
Set the max framerate to something like 80 (just to be sure it's slightly above the refresh rate) and enable Vsynch.
When your hardware can't push out enough FPS to match your monitor refresh rate you'll see the game stuttering. If you set the max framerate too high, your hardware will try to reach that number but will stutter even more. You shouldn't go lower than 60 anyway.
If the hardware can actually render more FPS than your refresh rate without problems, you'll see screen tearing (annoying lines) and Vysnch will take care of that.
If it's still slow, try lowering the Render Distance (something like 8-9 could become annoying).
Again, setting a higher value will require more power so the game could be slower.
If the FPS is dropping drastically after a while check your CPU/Video card temperature because if it's too hot, it will slow down to avoid damage. That usually happen when there's a lot of dust or if you're playing on a laptop.
It could also be caused by chunk errors (that you can see in the console if you keep the loader active) but that bug should have been solved back in 1.6.2/1.6.4.