Yes and No. You don't have to use FoodSaver brand bags, you can use other brands. I use Great Value from Wal-mart. But you can't use normal plastic bags, even the bag that manufactures use to package their food. The bag has to be designed for a vacuum sealer.
The reason you have to use bags designed for vacuum sealers is such bags have one smooth side and one textured side with the latter allowing the air to channel out. On a regular bag, both sides are smooth and this often causes certain spots to not get vacuumed out thereby defeating the purpose. Plus, some regular bags are too soft or too thin. This will cause it to melt during the "Seal" process.