St Patrick's Day (March 17th) is probably the most recognized of the many Feast Days, followed closely by St Valentine's Day. This was a day set aside to commemorate an individual who was instrumental in spreading the good news of Salvation to an, as yet, untapped area of the world, Ireland. Though it is, as in many cases, quite unique how God brought about this occurrence. St Patrick was born in 387 AD to a rich family living on the island of Brittania (England) back when it was still controlled by the Romans. When he was about 16 years old he was abducted by Irish raiders and taken into captivity in Ireland. According to his Confession he had a dream where God told him to escape from his captivity and go back to Brittania. He successfully escaped and eventually made it a monastery in Gaul (France) where he studied to become a priest. In 432 he had another dream where God told him to go back to Ireland and spread the Gospel to the Pagan, Polytheistic, people living there. One noteable aspect of St Patrick's teaching methods was to use the shamrock (clover) to explain the Trinity.
One thing is certainly obvious when looking at this example of God's providence and mercy is how we can see God's hand throughout St Patrick's entire life and how He brought about His plan to spread His message of Salvation to another corner of the world. And as part of the observance of the feast day of St Patrick we can praise God and give Him glory for another miraculous example of faith and mercy. Of course it is not really miraculous for God, it just seems that way on a human level.
But what about what this feast day has become? What started out as a commemoration of the life of St Patrick became more of a celebration of Irish culture and heritage, and ultimately another "drinking holiday." Of course how you decide to celebrate is a matter of personal preference, but it is important why you are celebrating. As a Christian really the only reason to celebrate is to bring glory, honor and praise to God for the good work He accomplished through his servant, St Patrick. If it is just another reason to drink alcohol, and possibly get drunk, then some addition consideration should be made toward celebrating at all. There is nothing wrong with imbibing in alcoholic beverages as long as it is done in moderation. After all, you get an exemption from the Catholic Church during the Lent season's requirement of abstaining from drinking alcohol, so why not take advantage of it?
In regard to celebrating Irish culture, it seems rather odd that this should be celebrated on this holiday considering St Patrick was not even born in Ireland. Yes, St Patrick did become the Patron Saint of Ireland, but the focus is, arguably, in the wrong place when observing this feast day.
To reiterate, the only reason for a Christian to observe this feast day is to praise God for the work He did through St Patrick, in Ireland. Any other reason would be a waste of time.