By default, syncing your iPod or iPhone through iTunes will move all your music, videos and podcasts onto the device. If the device doesn't have enough room for all your files, however, it will cut off, leaving some unsynced. Rather than leave the decision to chance, you can deselect songs you don't want, freeing up room for others. ITunes offers a few ways to remove unwanted songs, despite it initially appearing like you can't uncheck them.
Unchecking Single Tracks
When you open the music tab under the "Devices" header in iTunes, the check boxes next to each song appear grayed out and won't let you uncheck them. This music list simply displays the current contents of your device and can't be used to modify it. Instead, click the "Music" tab under the "Library" header. From here, uncheck the boxes by each song you don't want to sync. Click on your iPod, then check the "Sync only checked songs and videos" box. Press "Sync" to remove the unchecked songs from the device.
Selecting Song Groups
For large libraries, unchecking individual songs can take a long time. Instead, click on your iPod, then open the "Music" tab on the top bar of iTunes instead of the sidebar. Change the sync setting to "Selected playlists, artists, albums and genres." On this screen, check the box by each group of tracks you want synced to your iPod. You can also combine this with the individual song check boxes to sync an entire album or genre except for specific tracks.
After selecting your desired song groups, you may have space left over on the iPod. Rather than leave the space empty, iTunes offers the ability to automatically fill the remaining space with a random selection of songs. Check the "Automatically fill free space with songs" box on the Sync Music selection window, then press "Sync." Note that because this will randomly add songs during each sync, syncing will take longer to perform than without the feature.
If you want to have the highest level of control over the tracks on your iPod, check "Manually manage music and videos" on the Summary tab of your device on iTunes. This will unlock the music list on your iPod, allowing direct deletion of tracks from the device. This setting also prevents automatic syncing, so to add new tracks, drag them from your library to the iPod.