Someone asked for this before, and its become a fairly frequent topic on the board... So I thought I'd try to put this all together in a single posting - obviously the idea would be to "sticky" it and update over time as info comes available. As people respond or new info is posted I can update the first post accordingly...
I need good pics for the location of SNs on M3 and M5 Stuarts and M4/M4A1/M4A2 Shermans, tank destroyers,
Neil
M1 Abrams
Abrams SNs often start with a "D" for the Detroit Tank Arsenal, or "L" for the Lima Army Tank Plant. Others do not have these letters.
Full-Scale Engineering Development (FSED) Pilot Vehicles (PV) may not have the SNs in these locations.
SN is usually most easily found on the skirts.

(Dontos)

(Joe D)

(Jeff Button)
Rear hull, beside the right tail-light - SN above, Registration Number (RN) below.

(Jeff Button)

(Joe D)
Rear Engine deck

(Jeff Button)
Turret numbers can also be found

(Jeff Button)
M2 Medium Tank
Front & rear lugs.

(Joe DeMarco)
M2 and M3 Bradley
Near the frontmost left-side lifting point. M2 SNs should start with 2AA, M3 SNs should start with 3AA.

(Jeff Button)
M3 Lee / Grant
Front & rear tow lugs

(Joe DeMarco)

(Jeff Button)
M3 Stuart
Front right differential bulge
M4 Sherman
From the Sherman register:
web.inter.nl.net/users...serial.htm
M4 and M4A1
The tank serial number is only stamped on a plate attached to the lower left hull plate.
Canadian M4A1 Grizzlies have the serial or shop number stamped just below the hull caster's logo on the front of the hull. Look for a number between 1 and 188.

(Joe DeMarco)
M4A2
The tank serial number is stamped on the two rear tow points.
M4A3
On Ford-built M4A3s, the Ordnance serial number & Ford are stamped on the four corners of the upper hull - front and rear. The smaller of the two numbers is the Ordnance s/n, the larger is the Ford s/n.

(Joe DeMarco)

(Joe DeMarco)
On Fisher-built M4A3s, the SN can be found on the differential housing (as highlighted by the black circles in the first picture)

(Joe DeMarco)
On the ultimate generation M4A3s built by Grand Blanc Tank Arsenal, the serial number is stamped on the two rear tow points. The Detroit Tank Arsenal tanks are rather problematic. Some of their vehicles have the serial number stamped on the two rear tow points, while others lack any serial number markings other than on the data plate.

(Jeff Button)
The registration number (RN) can often be found on the right front of front hull - near the MG mount, it is the larger of the two numbers on the bottom.

(Jeff Button)
M4A4
The vehicle serial is stamped on each boss to which the towing shackle is attached.

(Sherman Register)
M5 Stuart
Right front hull
M10 Wolverine
Rear tow lugs
M26 Pershing
Rear tow lug

(Jeff Button)
M36 Jackson
On M36B1s, the SN can be found on the rear tow lugs as on other Sherman hulls.

(Jeff Button)
M47 Patton
Right front tow lug

(Jeff Button)
Many M47s, even ones now in the United States, will have rebuild plates from Italy

(Jeff Button)
M48 Patton
Stamped into the front right area on the hull, just under the headlight

(Jeff Button)
M50 Ontos

(Dontos)
M60

(Joe D)
Left front tow-lug

(Neil Baumgardner)

(Jeff Button)
Rear upper deck

(Jeff Button)
M60s often have two sets of SNs stamped on the rear engine deck. The originals crossed out, and the rebuild SN added. If the SN ends with an "A" it was rebuilt at Anniston Army Depot, if it ends with an "M" it was an Mainz Army Depot rebuild.

(Jeff Button)

(Joe D)
M113
Registration numbers can be found on the front hull under the headlight

(Jeff Button)
above the ramp

(Jeff Button)
and on the side ramp door

(Jeff Button)
M114
Left rear side below the upper lifting eyelet.

(Dontos)
Registration number can be found stamped into the hull, below the front left headlight

(Jeff Button)
M728
Rear deck, like on M60s

(Jeff Button)