How to get rid of Manipulate frame?

There is an option called Paneled to control the outer frame. Setting this option to False should do the trick.

Manipulate[Plot[Sin[x (1 + a x)], {x, 0, 6}], {a, 0, 2}, Paneled -> False]

To remove only the outer panel keep the frame around the content area, you can use Style + DefaultOptions as follows:

Style[#, DefaultOptions -> {Panel -> {Background -> White}}] & @
 Manipulate[Plot[Sin[n x], {x, 0, 2 Pi}], {{n, 3}, 0, 10, 1}]