Currently there are only 2 states (as far as I know) which prohibit sticking GPS and other stuff on the windshield - California and Minnesota.
California law (effective January 1, 2009) permits it, but only in a 7" x 7" corner of the lower right or the 5" x 5" corner of the lower left portion of the windshield. You can have a stem (goose-neck or otherwise) as long as you want it to be, though.
http://www.dmv.ca.gov/pubs/vctop/d12/vc26708.htm
(12) A portable Global Positioning System (GPS), which may be mounted in a seven-inch square in the lower corner of the windshield farthest removed from the driver or in a five-inch square in the lower corner of the windshield nearest to the driver and outside of an airbag deployment zone, if the system is used only for door-to-door navigation while the motor vehicle is being operated.
Minnesota prohibits stuff being stuck to the windshield (cops exempted, of course), or even suspended in any way between the windshield and the driver, regardless of where it's anchored. However, it
does allow for a GPS to be mounted to the "bottommost portion" of the windshield.
https://www.revisor.mn.gov/statutes/?id=169.71&format=pdf
169.71 WINDSHIELD.
Subdivision 1. Prohibitions generally; exceptions. (a) A person shall not drive or operate any motor vehicle with:
(1) a windshield cracked or discolored to an extent to limit or obstruct proper vision;
(2) any objects suspended between the driver and the windshield, other than:
(i) sun visors;
(ii) rearview mirrors;
(iii) driver feedback and safety-monitoring equipment when mounted immediately behind,
slightly above, or slightly below the rearview mirror;
(iv) global positioning systems or navigation systems when mounted or located near the bottommost portion of the windshield; and
(v) electronic toll collection devices; or
If Michigan has recently passed a law regarding GPS units, they've kept is very quiet, so quiet that it's not even to be found in the state laws of vehicle code. However, they already have a law that can, of the cop so chooses, apply to GPS units (Michigan has a lot of those "if the cop so chooses" laws).
http://www.legislature.mi.gov/(S(kkauo445uodnmqrymp2n0yz4))/mileg.aspx?page=getobject&objectname=mcl-257-709
(c) An object that obstructs the vision of the driver of the vehicle, except as authorized by law.
(1) A person shall not operate a motor vehicle with any of the following:
(c) An object that obstructs the vision of the driver of the vehicle, except as authorized by law.
The "if the cop so chooses" part is the determination of whether or not the object "obstructs the vision of the driver". But there are plenty of states which have similarly worded statues, including New Jersey, which prohibits driving a vehicle,
"with any sign, poster, sticker or other non-transparent material upon the front windshield, wings, deflectors, side shields, corner lights adjoining windshield or front side windows of such vehicle other than a certificate or other article required to be so displayed by statute or by regulations of the commissioner."
Section 21-1104 of the Maryland Code prohibits driving a vehicle "with any sign, poster, card, sticker, or other nontransparent material on the windshield, side wings, or side or rear windows of the vehicle." Part (2)(i) of this section permits attaching an object within a seven-inch square at the bottom of the windshield.
