There have been numerous clinical trials looking mainly at death, stroke, and cardiac outcomes related to omega 3 consumption, either in food or in supplements. Now the Cochrane Library has published the largest systematic review of these studies to date. Unfortunately, the review shows little benefit from consuming omega 3 fatty acid. This is a fairly extensive review with good statistical power:
The benefits of omega-3 fatty acids (EPA and DHA), which are found in fish oil, have been supported by repeated double-blind clinical trials. In 2004, the FDA announced qualified health claims for omega-3 fatty acids, noting supportive but not conclusive research that shows that consuming EPA and DHA omega-3 fatty acids may reduce the risk of coronary heart disease. Our Fish Oil includes 200mg of omega-3 fatty acids from EPA and DHA.
Haberka, M., Mizia-Stec, K., Mizia, M., Janowska, J., Gieszczyk, K., Chmiel, A., Zahorska-Markiewicz, B., and Gasior, Z. N-3 polyunsaturated fatty acids early supplementation improves ultrasound indices of endothelial function, but not through NO inhibitors in patients with acute myocardial infarction: N-3 PUFA supplementation in acute myocardial infarction. Clin.Nutr. 2011;30(1):79-85. View abstract.

It exists in nature in three forms, one derived from land plants and two derived from marine sources. In the body, omega-3 is highly concentrated in the brain; it is critical to the formation and maintenance of nerve cell membranes. Research shows that in the nervous system, omega-3s foster the development of brain circuitry and the processing of information. They also play important roles in stabilizing mood and staving off cognitive decline. Low levels of omega-3s are linked to poor memory and depression. Omega-3 fats are also critical for the formation of anti-inflammatory molecules in the body.
Why would someone foul a perfectly good box of rotini with omega 3 oils? This is based on the belief that omega 3 fatty acids reduce heart disease and vascular risk, probably through reducing blood pressure and cholesterol. This is a plausible claim, but as we see over and over again in medicine, plausibility (while nice) is insufficient as a basis for clinical claims.
Muñoz MA, Liu W, Delaney JA, Brown E, Mugavero MJ, Mathews WC, Napravnik S, Willig JH, Eron JJ, Hunt PW, Kahn JO, Saag MS, Kitahata MM, Crane HM. Comparative effectiveness of fish oil versus fenofibrate, gemfibrozil, and atorvastatin on lowering triglyceride levels among HIV-infected patients in routine clinical care. J Acquir Immune Defic Syndr 2013;64(3):254-60. View abstract.
A number of trials have found that omega-3 PUFAs might reduce anxiety under serious stressful situations. Case-controlled studies have shown low peripheral omega-3 PUFA levels in patients with anxiety disorders.27-31 A cohort study found that high serum EPA levels were associated with protection against posttraumatic stress disorder.32 In studies of therapeutic interventions, while a randomized clinical trial of adjunctive EPA treatment in patients with obsessive-compulsive disorder revealed that EPA augmentation had no beneficial effect on symptoms of anxiety, depression, or obsessive-compulsiveness,33 a randomized clinical trial involving participants with substance abuse showed that EPA and DHA administration was accompanied by significant decreases in anger and anxiety scores compared with placebo.34 In addition, a randomized clinical trial found that omega-3 PUFAs had additional effects on decreasing depressive and anxiety symptoms in patients with acute myocardial infarction,35 and a randomized clinical trial demonstrated that omega-3 PUFAs could reduce inflammation and anxiety among healthy young adults facing a stressful major examination.36 Despite the largely positive findings of these trials, the clinical application of the findings is unfortunately limited by their small sample sizes.
Heart disease. Eating fish can be effective for keeping people with healthy hearts free of heart disease. People who already have heart disease might also be able to lower their risk of dying from heart disease by eating fish. The picture is less clear for fish oil supplements. For people who already take heart medications such as a "statin" and those who already eat a decent amount of fish, adding on fish oil might not offer any additional benefit.