What's the purpose of this red marking on the fuselage of a Boeing 737?
@SMSvonderTann is correct. The marking is there for warning ground personnel about engine hazrd. In this photo (of a 737) you can see 'INGESTION HAZARD' written above the line. 



Image from airliners.net

In this image it is possible to zoom in to see it much more clearly. Note that this marking is not found in all 737s. The danger area is marked with two lines- one in forward fuselage and another in the engine, as can be seen in @mins photo, which I've put below.



Image from airlinereporter.com

Also, as @mins notes, the lines in 747 are for equipment positioning (to prevent damage to fairing, looks like)