Ubuntu provides the "USB Startup Disk Creator" tool to create a USB flash drive bootable image from the Ubuntu ISO images that can be downloaded from http://cdimage.ubuntu.com/releases/.
To use this tool, insert a FAT formatted USB stick, download a USB ISO image and then start the tool using: System->Administration->USB Startup Disk Creator and then enter you password.
You then select the ISO image you've just downloaded and make sure one has the correct USB flash drive selected. Then hit the "Make Startup Disk" button and after a few minutes you have a bootable USB flash drive equivalent to the ISO CD-ROM but with the extra bonus that it has persistent storage to save your documents and settings.
However, nowadays USB flash drives come in at 4GB to 16GB formats, so you have plenty of space to do a full Ubuntu installation and allow you to install extra packages - just like a conventional HDD. Also, the image will boot up much faster than the "USB Startup Disk" method. It's also worth noting that spending a little more on a fast USB flash drive is worth it. I've been using a 4GB Buffalo USB flash drive for a while and it's fast - don't be a cheapskate and go for price over speed.
A Ubuntu installation on a USB flash device can be achieved in various ways - one way is to initially install it using QEMU and then to dd the QEMU image onto the USB flash drive. This will then provide you with a system that can be run just like any conventional Ubuntu system on a HDD.
The instructions for this technique are written up here https://wiki.ubuntu.com/KernelTeam/InstallonUSBkey - prepare to take ~80 minutes or more to create the basic QEMU image.
The cool feature of using QEMU is that one can create a clean image which can then be copied onto multiple USB flash devices - which is ideal for rolling out test images for friends to try out or for creating test images with new features for testing at conferences or sprints.