What OS are you using? Check that you have the correct (latest) driver for your printer available here: http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?lc=en&dlc=en&cc=us&product=1138346&
Select your OS and click Next. Uninstall the old driver and disconnect the data cable (for directly connected printers) before installing the driver. For those Windows OS versions that include the driver with the OS, if the driver isn't automatically, check Windows Update for new updates (check for Optional Updates).
Are you getting any error messages (flashing lights on the unit)? Paper jams or low ink could be the problem.
Since the printer is a USB printer, try a new USB cable or a different USB port on the computer. Try a direct connection if you use a print server or USB hub. Check that the USB ports are working with a known good device. (For Windows, check if the USB ports are active. They can be turned off for security or power savings. The first is under the Device Manager (also check the driver status for the USB itself); the second is part of the Advanced Settings from the Screen Saver.)
Are the print jobs going to the queue and staying there? What is the printer status? For Windows, see the Devices and Printers Control Panel (older versions of Windows gave Printers and Faxes, IIRC). Try clearing the print jobs. For Windows, you can force this to empty by stopping and restarting the print spooler. Use the Command Prompt (for Vista and Win7 right click and choose Run as Administrator) Start > All Programs > Accessories > Command Prompt.
Type "net stop spooler" at the first prompt without the quotes followed by enter. Type Y if you get a warning about stopping the Fax Service. On the next line, type "net start spooler" again without the quotes and then hit enter. When you get a third prompt, restart the computer. Then check your printer queue. (You could do only the first step and then restart; however, you will need to go for a coffee break after the restart.)
Once the queue is empty, try a new print job. Next try resetting the printer. Unplug the printer (from both the computer and the outlet) and remove the data cable (from both the computer and the printer). Wait a short while and then reconnect everything. Try printing again.
Try printing a different type of file from another program. For example, PDFs sometimes won't print from Adobe Reader. This could result from a damaged PDF, a problem with Adobe Reader or something else. You can try using the Advanced Printer Properties (click the box when you select which printer you want to print to) and try printing the document as an image. Also try printing the same document from another computer/printer (transfer it to external media if you use another computer to minimize additional file transfer damage).
I hope this helps.
(BTW if you use a Mac, do not delete jobs from the Print Queue. Instead press Cancel at the printer. Otherwise, your computer may lose the connection to the printer.)