Yes eventually you will need a new battery. The iPad 2 started with a 10 hour battery life and it will get shorter and shorter until eventually you will only be able to used it plugged in, similar to many laptops. The need for a new battery will become evident when it starts shutting down before the battery indicator gets to zero. Depending on your tolerance you may be able to live with this for awhile. My iPhone 3GS is over four years old and it eventually needed a new battery. A new battery with instructions from the internet brought my iPhone back to life for very little money.
I also have an aging iPad 2 that has been used daily for the last 2 and 1/2 years. It still seems to have very good battery life. I would not worry about the battery.
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.