Assuming the fish is prepared properly and is sushi grade, how many times per week can I eat sushi without having to worry about mercury poisoning and/or health concerns? I'm not sure if the kind of fish is important, but I generally eat salmon, white tuna, and yellowtail.
Provided you go to a reputable sushi restaurant with good hygiene standards, you should have no problem in terms of bacteria or parasite-related health problems. Most fish used in sushi restaurants is flash-frozen at -20 degrees C (-4F), which kills parasites outright.
As for mercury, you can check the FDA's page detailing the amount of mercury in the various species of edible fish, to help you make an informed decision. They recommend that higher risk groups, such as pregnant women, limit their intake of certain fish to 12oz/week.
Generally, sushi is extremely healthy as it is low in fat and high in vitamins and minerals - Japan has the highest life expectancy in the world, after all: diet plays a big part in that.