Nice thread, I agree to the fact that most manufacturers mint money of customers by stating the fact that the particular part isnt under warranty. And its nothing but stories and people just pay the bills and come back.
Well, I have taken very few warranty claims and let me put them here..
1. Volkswagen Polo
Problem: Compression leak from exhaust side of engine head at 11k kms on clock..
Solution: took 3 visits to ASC to diagnose the problem and complete HEad assembly (excluding camshaft) was replaced under warranty. Billing was 1.3 Lacs excluding labour and taxes. Time taken by ASC, 9 days and VW refunded us taxi fare of some 8k for those 9 days..
Absolutely no problem in claiming warranty.
2. Cousin's Honda Civic
Problem 1: car used to consume over 1 L of engine oil in 5k kms
Solution: Ring Road Honda ASC showed us the owners manual where it stated that the car can consume upto 1 L of oil in 1k kms (Fine Prints, I tell you). And said good bye and thank you. On asking to take the oil out to measure the amount that comes out of engine, I was refused access to service area. Later I forced them to let me in. When I tried to take snaps, the adviser said: I let you inside service area, if you take any pictures, I will have to call the guards. Never in my life did I ever want to beat a service adviser soo badly..

On escalating the matter, even the GM told me that the oil consumption is normal. Cousin didnt want to take the matter up, chapter closed.. Later switched to Ide-Mitsui synthetic oil from Honda, the oil consumption went almost nil..
Hopeless Service..
Problem 2: Engine Mount gone bad at over 40k kms. Almost all civics here on team bhp have had their engine mounts changed within 30-40k kms and Honda has no answer. The part should have ideally been recalled..
Solution: Sir, its a rubber part not covered under warranty, you will have to pay Rs.8k including labour for the same.
Again why dont they add it as a replacement part in service intervals every 30k kms.
3.Mitsubishi Cedia
Problem: Airbag clock spring can go kaput any time, it can last for 1 year, or 2 year, 3 year or 4 year as in my case..Again a part for recall.
Solution: if the car is under warranty the company will replace it. If the car is not under warranty, you will have to shell Rs.12k from your pocket. Few BHPians got it changed under warranty but mr friend whose cedia was 3 year old and 38k kms on clock had to shell Rs. 12k. Brothers cedia 4 year old and 65k on the clock had to pay for this. My cedia 4 year old and almost 80k on the clock has this issue. Have seen N number of cars at the ASC which had their clock spring changed at owners cost. Bhpian sukrit escalated the issue with Mitsubishi for his 3 year old and 12k driven cedia and got 50% off on the part..But I have seen the company providing good will warranties outside warranty without problem if issue is escalated.
4.Maruti Swift
Problem: Hopeless clutch
Solution: owners had to change it within 10k kms and pay from their own pocket.. Ours though lasted for 52k kms..with some stretch..