The following list is an example of NSAIDs available: 

• aspirin
• celecoxib (Celebrex) 
• diclofenac (Cambia, Cataflam, Voltaren-XR, Zipsor, Zorvolex) 
• diflunisal (Dolobid - discontinued brand) 
• etodolac (Lodine - discontinued brand) 
• ibuprofen (Motrin, Advil) 
• indomethacin (Indocin)
• ketoprofen (Active-Ketoprofen [Orudis - discontinued brand]) 
• ketorolac (Toradol - discontinued brand) 
• nabumetone (Relafen - discontinued brand) 
• naproxen (Aleve, Anaprox, Naprelan, Naprosyn) 
• oxaprozin (Daypro) 
• piroxicam (Feldene) 
• salsalate (Disalsate [Amigesic - discontinued brand])
• sulindac (Clinoril - discontinued brand) 
• tolmetin (Tolectin - discontinued brand) 
• rofecoxib(Vioxx- discontinued brand)

How aspirin is different and prevents heart attack.

(from Internet)

In 1982, the British chemist Sir John Vane shared the Nobel Prize in Medicine in part for figuring out how aspirin worked, but some researchers now think that his work may have been only a good beginning.
Sir John discovered that aspirin blocks an enzyme called cyclooxygenase, or COX, and stops production of substances called prostaglandins that contribute to pain, swelling and fever when the body is injured. One prostaglandin, called thromboxane, is produced in tiny blood cells called platelets, and causes them to adhere to one another and plug up any sites of bleeding.
Aspirin is one of the rare magic bullets in medicine when it works against thromboxane: even tiny doses completely and irreversibly stop thromboxane production.
People who take a baby aspirin a day for 10 days have no thromboxane at all left in their platelets. Although their blood will still coagulate normally, their platelets do not stick together well, and they may bleed a little more from a cut or scratch than usual. It takes a full 10 days for aspirin's effects to wear off after a person stops taking it.
In contrast, other anti-inflammatory drugs like ibuprofen and naprosyn stop thromboxane production for only a few hours at a time and have far less potent effects on platelet stickiness than aspirin does. Tylenol has no discernible effect on thromboxane at all; nor do the new ''COX-2'' arthritis drugs like Celebrex (celecoxib) that block only a nonplatelet variant of the enzyme.
Surveys estimate that hundreds of thousands of Americans think that if aspirin works for the heart, then all these other similar medications must certainly work too. In fact, not one of them has been shown to have the beneficial effects on the heart that aspirin does.
For many years scientists have ascribed aspirin's exclusive heart benefits entirely to its dramatic effects on thromboxane and platelets.
Heart attacks begin when a cholesterol plaque shears off the inner wall of a blood vessel in the heart: platelets rush in to repair the damage, and often wind up plugging the vessel completely in the process, stopping blood flow and causing heart muscle to die. In a person taking aspirin regularly, the platelets should slide smoothly right past the ruptured plaque, allowing blood to continue flowing through the damaged vessel.
But now researchers are wondering whether eliminating platelet stickiness is really the final answer in the aspirin story.
New evidence shows that inflammation in the coronary arteries may also contribute to heart attacks, possibly by making cholesterol plaques unstable so they are more likely to detach from the vessel wall and cause blockage. Thus, it is possible that some of aspirin's anti-inflammatory effects may also help the heart.
In a study published in The New England Journal of Medicine in 1997, Dr. Paul Ridker, a Harvard cardiologist who directs the center for cardiovascular disease prevention at Brigham and Women's Hospital in Boston, found that tiny elevations in blood levels of a protein called CRP could powerfully predict who among a group of healthy middle-aged men was likely to get a heart attack. CRP is an indicator of inflammation in the body, and Dr. Ridker's study found that in men with high CRP levels who took aspirin regularly, blood levels of CRP and risk for heart attack fell sharply, in parallel.
Last month another study by Dr. Ridker's group in The New England Journal of Medicine showed that CRP levels could also predict heart attacks in women.
In Dr. Ridker's vision of aspirin as a heart drug, it works not only because of its effects on thromboxane and platelets, but also because it stops inflammation in a variety of ways, many of which appear to have nothing to do with COX and prostaglandins.
''What fascinates us is that if aspirin has a role in the heart as an anti-inflammatory agent as well as an antiplatelet agent, and if we can understand that pathway better, we might be able to come up with an even better way to hit that target,'' Dr. Ridker said. ''From where I sit, the fundamentally interesting part of this whole field is what we don't yet understand about aspirin.''

Difference between COX1 and COX2

Different types of prostanoids can be easily synthesized in the body by using an enzyme named as cylcooxygenase (COX). These prostanoids including prostaglandins, prostacyclin and thromboxane are important biological mediators that play crucial role in the development of pain and inflammation in the body. So it is possible to get relief from pain and inflammation by inhibiting the COX enzyme.

There are three different types of COX enzymes such as COX1, COX2 and COX3. They are similar in different aspects and have some differences too. The difference between COX1 and COX2 is outlined below.

Difference in Name:

COX-1 is also called as constitutive enzyme because it is produced by a cell under all types of physiological conditions. The amount at which constitutive enzymes are produced remain constant without regard of substrate concentration and physiological demand. On the other hand COX-2 is an inducible enzyme as it is produced under certain specific conditions like inflammation.

Difference in Locations:

COX-1 is commonly found in the kidney, stomach and platelets whereas COX-2 is located in macrophages, leukocytes and fibroblasts.

Difference in Functions:

COX-1 play important role in housekeeping such as it protects gastric mucosa, regulate gastric acid and maintain normal functions of the kidney by stimulating prostaglainds.  COX-2 is involved in the synthesis of prostaglandins that causes pain and inflammation in the body. Other function of COX-2 are protection from

Difference in Production:

The stimulation of COX-1 enzyme is done on a continuous basis by the body but COX-2 enzyme didn’t present at normal condition and produced only at the time of need. The stimulation of COX-2 enzymes is dependent upon cytokines.

Difference in Usefulness:

COX-1 enzymes are protective in nature and therefore are useful for the body. So there is no need to inhibit them but COX-2 enzymes play an important role in inflammation and pyrexia. So it is desirous to inhibit COX-2 enzymes.

Difference in Inhibition:

There are different types of drugs that are used to inhibit COX-2 enzyme including Celecoxib. Nonsteriodial antiinflammatoru drugs inhibit both COX-1 and COX-2 enzymes.

What is surprising is that taking NSAIDs just 1-7 days increases the risk of heart attack by 92%.

I don't believe most physicians, not to mention the lay people, are aware of that 

although we've been aware of the risk for a long time.