Instead of carrying a DVD, I would like to load a bunch of movies onto a flash drive then carry the flash drive around. When I want to watch a movie, I would like to plug the flash drive into a TV or a laptop computer and watch my movies.
Bruce's answer more or less covers it all, but for best compatibility, try to get a USB 2.0 drive with a fast transfer rate. You may also find that some TVs (particularly older ones) may have limits on the total size of drive they will recognise.
You can get video players/streamers which will allow you to plug the drive into them and will transmit the result onto the TV, but that's really only of use for fixed installations (if you're going to start carrying around a USB drive, streamer and cables and connect it up as you go along, you might as well take a laptop with you).
As for Kalista's suggestion, Google's Chromecast is brilliant, but it doesn't do what you are after. Instead, it allows you to stream content for a PC/Mac/tablet to the TV (or from the internet, under control of the devices) so it doesn't allow you to plug in a USB drive directly.
The best device to help is google's chromecast: http://www.google.com/intl/en/chrome/devices/chromecast/?gclid=CPq2tO-0l7wCFchhfgodngQACw
Some TV accepts certain size of external hard drive or USB key, this also an come in role.
You can do this with pretty much any modern computer today - desktop or laptop - without any extra effort. The TV may present issues. Some televisions only recognize specific video containers and codecs which can lead to them not "seeing" those files or being able to play them. There will also be limitations regarding the filesystem used on the device.
For example, I have a Scepter TV that has a USB port but it only recognizes .mp3 audio files as well as .jpg pictures (baseline), but does not do video at all. It also only recognizes FAT32 or FAT16 filesystems on the USB device. I have seen some that also recognize ExFAT. Be aware that some USB devices are preformatted with ExFAT instead of FAT32.
Thanks for your answers. I also heard that there is a device out there in todays market that translates the information on the USB flash drive into viewable media. Is this true?
Are you referring to chromecast ?