This is a job for the third-party software development community. Many small applications exist that have been written for iTunes on both Windows and the Mac, intended to support exactly this feature. Reading in the artists and albums from your iTunes Library and searching likely locations on the web for appropriate album art, you can then embed into your songs with a single click.
Download an Appropriate Album Art Finder Program
If you're a Windows user, go to http://www.ipodsoft.com/index.php?/software/iart to find the download page for the iArt program. iArt is shareware and costs $10 for registration, without which only a limited number of album cover retrievals is possible.
Mac users might like CoverScout, which you can find at http://www.wuffwuffware.com/products/CoverScout.html. This program is shareware, with an $8 registration fee. (Without this registration, you can search for album art for only the first 10 albums in your iTunes Library.)
Install the Program
After the program is downloaded to your computer, follow the included instructions for installing it.
CoverScout, like most Mac applications, comes packaged in a disk image. Install the program by dragging the CoverScout icon from the disk image window to your Applications folder.
iArt, like other Windows-based album art finder programs, requires that you install the .NET framework, available as a free download from Microsoft. (iArt's installer program automatically downloads and installs .NET for you.)
Search for Album Art
Both applications discussed here work in much the same way. When you run the album art finder program, it searches your iTunes Library for a listing of artists and albums that don't already have album art. Select one of these album entries that doesn't have art in the tracks already. (CoverScout uses an ! icon to show tracks and albums that don't have artwork, and iArt automatically moves through albums one by one that so you can either save the album art it locates or skip the album).
Use the program's built-in facility to search selected sites for appropriate album art. Both CoverScout and iArt allow you to search Amazon.com, Google, and the iTunes Music Store. In CoverScout, use the buttons in the toolbar to choose a source to browse for album art, and then click Get Artwork to perform the search. In iArt, select the Automatic Internet Art Retriever option, choose a searching source from the drop-down menu, and then click Next to begin searching the selected source for art for each album in turn.
Add Album Art to Selected Tracks
If the program finds album art, it's a matter of a single click to add it to the selected tracks. In CoverScout, use the Set button in the toolbar to apply the images to the selected album; in iArt, use the Save Result Next button to apply the image and move on to the next album.
As you continue using CoverScout, you can refresh the list of albums to show only those entries that haven't yet had artwork applied, repeating the process until you've finished adding artwork to all the albums in your collection. iArt continues processing your albums until you've added album art to all your albums or you've skipped them using the Skip Album button.