I have come to know about various Passenger Trains (Sawaari Gaadi as in Hindi) from my trips & sites like IRI. They stop at many stations but less than EMU/MEMU/DMU Trains. The Fast Passenger(FP) Trains stop at many stations but comparatively less than Passenger Trains. The advantage of running such Inter Town Trains on sections of Trunk & Non-Trunk but congested routes is that some Superfast & Mail-Express Trains can then skip these stations to avoid short distance passengers. Some "Passenger"(P) trains which I have come to know about are :-
Gomoh-Mughalsarai P, Lucknow-Saharanpur P, Allahabad-Mughalsarai P and Kolkata-Chittranjan FP(To be extended uptil Deoghar) ... :-D
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PS: Himgiri Express(& many more trains) runs Non-Stop between Howrah & Asansol as this section is...
Read more... quite rich in running EMUs, MEMUs, P & FP Trains and also IC Exp Trains. It's only beyond ASN that this train has got many redundant stoppages right uptil Jammu Tawi as there aren't a good number of Local Trains on sections like Asansol - Patna, Mughalsarai - Patna, Lucknow - Varanasi via Sultanpur, Saharanpur - Ambala and Jalandhar Cantt - Jammu :-p