Try the reset. Hold down the sleep and home keys until you see the silver apple. let it reboot and try again
Try a different charger
Try a different cable
Try a different outlet
make sure you're using an iPad charger, not an iPod one. iPod and iPhone chargers put out half the power the iPad wants.
If you have a can of air, blow out the port, bit of dust or lint can mess with the connection and charging.
If you go through all that and it still won't charge, then it may be time to make an appointment at your local apple store and have them check it out. Those ports can go bad.
Try this first - Reset the iPad by holding down on the Sleep and Home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons. (This is equivalent to rebooting your computer.)
The quickest way (and really the only way) to charge your iPad is with the included 10W or 12W (5W on Mini) USB Power Adapter. iPad will also charge, although more slowly, when attached to a computer with a high-power USB port (many recent Mac computers) or with an iPhone Power Adapter (5W). When attached to a computer via a standard USB port (2.5W, most PCs or older Mac computers) iPad will charge very slowly (but iPad indicates not charging). Make sure your computer is on while charging iPad via USB. If iPad is connected to a computer that’s turned off or is in sleep or standby mode, the iPad battery will continue to drain.
Apple recommends that once a month you let the iPad fully discharge & then recharge to 100%.
How to Calibrate Your Mac, iPhone, or iPad Battery
At this link http://www.tomshardware.com/reviews/galaxy-tab-android-tablet,3014-11.html , tests show that the iPad 2 battery (25 watt-hours) will charge to 90% in 3 hours 1 minute. It will charge to 100% in 4 hours 2 minutes. The new iPad has a larger capacity battery (42 watt-hours), so using the 10W charger will obviously take longer. If you are using your iPad while charging, it will take even longer. It's best to turn your new iPad OFF and charge over night. Also look at The iPad's charging challenge explained http://www.macworld.com/article/1150356/ipadcharging.html
Also, if you have a 3rd generation iPad, look at
Apple: iPad Battery Nothing to Get Charged Up About
Apple Explains New iPad's Continued Charging Beyond 100% Battery Level
New iPad Takes Much Longer to Charge Than iPad 2
Apple Batteries - iPad http://www.apple.com/batteries/ipad.html
iPhone: Hardware troubleshooting (Power/Battery section also applies to iPad)
Extend iPad Battery Life (Look at pjl123 comment)
New iPad Slow to Recharge, Barely Charges During Use
iPad: Charging the battery
Best Practices for iPad Battery Charging
Tips About Charging for New iPad 3
How to Save and Prolong the battery life of your new ipad
Prolong battery lifespan for iPad / iPad 2 / iPad 3: charging tips
iPhone, iPod, Using the iPad Charger
Install and use Battery Doctor HD
To Extend a Device’s Battery Life, Get to Know It Better
iPad Battery Replacement
In rare instances when using the Camera Connection Kit, you may notice that iPad does not charge after using the Camera Connection Kit. Disconnecting and reconnecting the iPad from the charger will resolve this issue.