Seven near misses are one too many, but there are a few things to remember. First, at any given time there are between 6,000 and 8,000 airplanes in the air in the U.S. When you compare seven incidents to all the take offs and landings that take place in one month the number is very, very small. Second, all incidents have to be reported but that doesn't necessarily mean that every incident was almost an accident or that the two airplanes were 50 feet away from each other. Any deviation from the standard protocol has to be reported.
Having said that, near misses are definitely a problem. We have too many airplanes flying into large airports and many of the ATC people are tired. But there are many safeguards such as short shifts for ATC personnel or the fact that all aircraft have a TCAS system that tells them when an airplane is too close. I wouldn't be too concerned, though. Flying is still extremely safe (when was the last time you heard about two airplanes crashing in mid air).
They call near misses when then approach too close, but not to represent an inmediate danger. With the TCAS, the risk virtually non existent. The only concerned is in countries with a lack of radars, in which planes don´t normally have TCAS and, light planes don´t have the transporder on.
As far as Europe and America, all planes should have TCAS fitted. So I wouldn´t get too concerned for this issue.
You have a much greater chance of hitting a car on the way to the airport then your plane hitting another. Every day, in the US alone, 5000+ airplanes are in the sky during the daytime. In fact, here are the latest stats from http://flightaware.com
Tracking 5,074 airborne aircraft with 45,035,395 total flights in the database. FlightAware has tracked 49,405 arrivals in the last 24 hours.