No. The amount of space on your device is fixed when you buy it. The only exception is Music, where if you choose to subscribe to iTunes Match, your music library will be availble to download an play on your device any time you have an internet connection without needing to store it all on your device.
If you want to save space, you'll have to use iTunes to sync some of your data off your device to make room for other data. You can also import your photos and videos to your computer and delete them from your camera roll to save space (see http://support.apple.com/kb/HT4083).