Check these locations:
Below the barrel stamped into the crankcase. On the front of the engine stamped either side of the crankcase join. Below the clutch / transmission area. Rear of cases below carburettor area.
By far the most common location is on the steering head. It may also be found on one of the rear downtubes or on the front downtubes.
Other locations include: top tube below fuel tank; lower frame rails; swing-arm pivot area.
Motobecane Mobylette 1968: Forward of the rear wheel axle on left side.
AJS and Matchless
Jampot has sections on serial numbers.
The AJS Matchless Club UK
Ariel Serial Numbers
BSA Serial Numbers
BSA Frame Numbers at BritBike.com
BSA at sunnymeadcycles (PDF)
BSA C15 Serial Numbers
DKW Vehicle Identification
DKW NZ350 Serial Numbers
Frame & Engine Numbers
NSU Max - (1)
Also Automoto, Griffon and Meteore
Puch (See also Sears Allstate)
Puch moped chassis numbers Includes links to pages covering MS, MV, VS, VZ, SR, SRA and RL
See also under Penton
Sachs 98ccm Modell 1932
Terrot Serial Numbers
Velocette LE Engine & Frame Numbers
Velosolex engine serial numbers