I have a Porsche 944 that does not have the original engine that came
with the car. I need to identify the year of the engine itself, not
the car. Can you tell me first where to locate the ID number on the
actual engine and then how to determine the year of the engine.

Dear jreuter,

I assume that the engine that has been installed in your Porsche in
exchange for the original one is also a 944 engine. In that case, and
if the engine dates before 1988, the ID number is located on the
engine's left side (seen in driving direction), embossed in the
cylinder crank case, .
See this picture for the location of the ID number:
http://www.9ss1.dk/porsche944/ibog/007c.gif
Source: Original 1982 Porsche 944 Manual, on Anders Nissen's website

Starting with the '88 model engines, the ID number is embossed on the
rear right side of the engine.

For identifying the exact type and year of the engine, please use this
code chart. It derives from a German source, so here are the English
translations of the introduction and the most important terms:

"Decoding the Engine ID Number
Example: 41E 00456 
------------------------------------------------------------------
4 ==> Engine Type (4 = 4 Cylinder Engine) 
------------------------------------------------------------------
1 ==> Engine Model   
------------------------------------------------------------------
K ==> Model Year Code Letter. C=1982; D=1983; E=1984; F=1985...
      I and O had been omitted because of danger of confusion!
------------------------------------------------------------------
00456 ==> Serial Number 

Key terms used in the chart:
Zyl (abbreviation for Zylinder) = Cylinders
Ltr (abbreviation for Liter) = Cylinder Capacity, metric
PS (abbreviation for Pferdestärken) = Horse Powers
Modell = Model
Motornummer = Engine ID Number
Einbau-Jahr = Year of Installation

And here the ID Code Chart itself:
http://www.nize944.de/Info944/Motornummer_haupt.html
Source: Nize´s Porsche 944 Homepage, by Frank Nize


Sources:

Porsche 944 Website, by Anders Nissen (in Danish)
http://www.9ss1.dk/porsche944/index.htm

Porsche 944 Manual, on Anders Nissen's website (in German)
http://www.9ss1.dk/porsche944/instruks.htm

Nize´s Porsche 944 Homepage, by Frank Nize (in German)
http://www.nize944.de/

Search terms used:
motornummer 944
://www.google.de/search?q=motornummer+944&ie=UTF-8&oe=UTF-8&hl=de&meta=
Zylinderkurbelgehäuse 944
://www.google.de/search?hl=de&ie=UTF-8&oe=UTF-8&newwindow=1&q=Zylinderkurbelgeh%C3%A4use+944&meta=

Hope this helps!
Best regards,
Scriptor