What would you do if you'll get another job offer with a higher salary than your current job with an on-going contract? Resign or Stay? why?

I'd rather stay with my current job. It is true that distant pasture always look greener but... I believe that a rolling stone gathers no moss.  Life is a cycle... the moment you start with your new job, again another alluring offer will come along.  With that vicious cycle, time will come no company would be willing to hire you coz you have that reputation of no loyalty.

inform immediate superior about the offer to show professionalism but require a notice whether current employer will make a counter offer, otherwise file necessary notice of your planned resignation as required by law. Opportunities for advancement/improvement must be grabbed whenever they come your way but in such a way that your professionalism is evident

Some will go for the money. Do not fall prey to where the money is. What's important is, follow your area of expertise and happiness. No point working with high pay that don't meet up with your personal satisfaction. You'll be doom with bad testimonial. At the end of it, adhere to MASLOW law. Find something that better suit your personality and commitment. So if that other job better suits you, do approach your current employer for them to be able to find suitable replacement and follow up with whatever projects at hand. I agree with Crisanto, professionalism is an utmost value in a person and it'll bring a person to success.

Despite everything I say yes.

Yes of course. If a good offer is offered to me, i will definitely avail that opportunity.

At the end of the day "Pay Check" matters, but Commitment comes first, if you have valid contract with some company you must share your new offer to them and ethically ask them if they release you otherwise you have to fulfill your commitment with your current employeer.

If the new job falls within my profession. I would first communicate with my current employer informing them of the new offer. Depending on the contract period of the new I would tender a resignation notice (if contract exceeds two years) otherwise I would stick to my current job. If I have a few years before I retire, then, I would not even contemplate leaving my current job despite the salary difference

if i get such offer, i will inform my superior, in my opinion if your manager likes your growth in the company he will try to give you something within the company or he will try to release you, if he does not do any thing, it is better for me to give notice to company and as per rule, join the new company.

well, sometimes you have to be loyal to your employers. Talk to your employers about your new offer because they might give you a raise or a bonus if they think you are worth it. However, if they can not offer you anything more then you have the right to take the new offer. At the end of the day you need to think of your self but with out harming others.

Handover all relavant documents to the relavant team with respect to the project

yes off course, if i get good offer is offered to me, sure i will accept that offer ....