Not necessarily. Closing a disc session makes the disc compatible with other computers, but not all discs need to be closed. You only need to close CD-R, DVD-R, and DVD+R discs. Rewriteable discs (which end in RW) don't need to be closed. In addition, discs that have not been closed can still be used in other disc burners. They can't be used in CD-ROM and DVD-ROM drives, however.
Some programs might offer to finalize your disc instead of closing the current session. A disc that has been finalized is complete, and you can't add any more files to it. If you close the current session, however, you can add more files as long as you have room on the disc.
Mastered discs do not need to be closed; they are automatically compatible with other computers, so you will never see an option to close a session that you have made with the Mastered format. If you are burning a Live File System disc, however, you will need to close the current session to be able to use the disc in another computer or player (by default, Windows does this automatically when you eject the disc). Keep in mind that each time you close a disc session, some of the disc's space is used, so it's a good idea to only close a disc session if you expect to use the disc in the CD-ROM or DVD-ROM drive of another computer. If the disc will remain in your current computer, you don't have to close the disc session.