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My compact camera has a burst mode, which shoots 10 fps at 2 megapixels.
I plan to use it at an upcoming company sporting event (basketball and tennis, outdoors) and plan to post memorable moments at our company bulletin board and boardroom. That is, print the photos uncropped at 4x6 inches. I have a class 10 SD card.
Do I need (to shop for) a "better" camera?
As a rough rule of thumb, photos tend to be printed at a maximum of 300 dots per inch (dpi), but anywhere from around 240dpi will produce a print that looks sharp when viewed closely. 300dpi means that every 1" × 1" square of print is actually made up of a grid of tiny dots, 300 dots along each side (and therefore 90,000 dots in total).
A digital camera's sensor also captures a grid of dots. The dots are known as pixels and 1 megapixel = 1,000,000 pixels.
We now have all we need to do a simple bit of maths. :)
A 6x4" print at an optimum resolution of 300dpi will be made up of (6 × 300) × (4 × 300) = 2,160,000 dots: just a touch over 2 megapixels. However, to print at a perfectly acceptable 240dpi we only need (6 × 240) × (4 × 240) = 1,382,400 pixels.
Result: a 2mp camera should produce great 6×4" prints!
The answer to the simple question -Is 2MP high enough quality to print a 4x6? - Is yes.
Especially if these are just being used for "fun" display purposes and not in a professional manner. They also would be suitable for most online use.
Diving deeper in to the details of your question though, you are asking if your point and shoot camera is a good solution to take 4x6 printed photos of sports. 4x6 photos are not the problem, but you might run into issues with maximum shutter speeds not being high enough, causing blur in the images, or on the other end of the spectrum even a blown out image.
The big advantage of a DSLR or higher end camera, would be the ability to shoot at high frames per second, for longer periods, at a higher resolution. They also will do a much better job at focusing in on your subject, and be able to do all of this at a moments notice even when the camera is in standby mode. A compact or point-and-shoot camera likely will require you to prepare for the shot by keeping the camera on, and even pre-focusing before the "moment" to get the shot you desire. Otherwise you might end up with 10 frames that capture the moment right after all of the excitement.
In my opinion, I wouldn't rush out to go get a new camera or SLR. I would be comfortable taking shots with an iPhone 4 of an event like this, with the goal of printing a few 4x6 photos for other employees to view online or on a community board. Professional equipment is not a necessity, it just will allow you to do this in a more varied environment, to get crisper high resolution shots that can be printed larger or cropped more.
Update: The other answers here are correct in pointing you to PPI and DPI - but in my opinion, for non professional 4x6 use, just about any camera under the sun including most current cell phone cameras will produce just fine prints. I know people(my wife) who strip 72dpi Facebook images directly off the web and print them. They are perfectly acceptable to non-photographers who are expecting non-professional work.
This is all assuming the sports are played outdoors, or in very good indoor lighting. If the lighting is poor - you are going to have trouble with anything but professional equipment to do sports.
A good resource for translating megapixels into print sizes is here, but generally at 200 PPI* - the results should be OK.
There may be a whole host of other issues in shooting sports but it depends on your expectations. Your camera may not be able to focus fast enough and in general, shooting sports requires a good deal of anticipation of the action - but for a company event, if your expectations are modest, you may be ok.
*I bring up PPI here because you want a certain minimum quality. Anything you do for work - in your professional capacity or not - should meet a minimum standard. Good enough to just bother printing off Facebook to show the family and good enough to tell your boss 'I did this' should be different things.
