Hosting

Please note that the best alternative to all the hosting options described below is Your Own Hosting. The clear advantage is that you virtually have no restrictions in what material you can host. Pretty much the only disadvantage is that you have to pay a monthly fee, but even that can be very minimal.

Video Hosting
DO NOT USE VIMEO They kicked our asses out. Vimeo will delete any account with any videos of video games of any kind.

DO NOT USE VIDDLER They no longer allow you to make free accounts and their pay options are awful.

DO NOT USE BLIP.TV They randomly "purge" LP accounts. Or maybe not. They used to allow HD, but now that's pay-only or something.

YouTube
Pros:
 * Can host HD video.
 * Doesn't care about LPs.
 * No time limit for accounts in good standing. All you need to do is verify your account.
 * Immortal.

Cons:
 * Encoding videos for YouTube can be a somewhat strange process.
 * No option to download source video.
 * Depending on the developer, the day, the moon's alignment, and depending on if the bug you stepped on this morning cursed your name with its dying cough, your LP could indeed be targeted and blocked in some countries, if not flat out deleted. It's very inconsistent really.
 * 15 minute time limit for those not graced with no time limit, although that's pretty decent.
 * Shunned community. Can be avoided by unlisting your video and/or turning off comments. Could be considered a pro from a different perspective.

Dailymotion
Pros:
 * Can host HD video.
 * Doesn't care about LPs.
 * Unlikely to die any time soon.
 * A decent alternate video host.

Cons:
 * 20 minute time limit.
 * No option to download source video.
 * Lots of intrusive ads.

Self-Hosting
Read the Self-Hosting Your Own Video LP guide for more information on how to do this.

Pros: Cons:
 * Nearly unlimited possibilities - depending on how much you pay for hosting.
 * Not free
 * Not easy to use
 * Limits vary by actual hosting provider

Image Hosting
DO NOT USE IMAGE SHACK It does not work on SA.

DO NOT USE PHOTOBUCKET It will run out of bandwidth very fast. It will also make it easy for people to find out how big a creepy fuck you are.

DO NOT USE WAFFLEIMAGES WaffleImages was shut down. Thank you R1CH and all the others who contributed to the project.

LPix
Pros: You'll need Microsoft C++ 2010 Redistributable (x86) (x64) for the newest version. Make sure to insert your LPix username and password in the plug-in options or it won't work.
 * LP exclusive image host run by baldurk. Give the man a hi5 if you see him.
 * Lets you sort images into separate galleries.
 * Powered by baldurk's pro voice.
 * Has a Rightload plug-in.

Cons:
 * 2MB max file size upload limit.
 * Makes every other image host look like a busta.

Minus
Pros:
 * Supports most file types
 * 15 MB file size upload limit.
 * Unlimited downloads.
 * Free accounts, starts at 10 GB space, can be upgraded to 50 GB.
 * Has a set of applications for several different platforms to facilitate uploads.

Cons:
 * Apparently requires you to log in using Facebook/Twitter and allow it to post messages to your feed, or download a mobile app and use that?
 * Guest uploads expire in 30 days?
 * Hot linked images may be throttled?

Imgur
Pros:
 * Supports a lot of different image types.
 * Has a Rightload plug-in.

Cons:
 * 10MB max non-animated, 2MB animated file size upload limit.
 * If non-animated image is over 1MB then it will automatically be compressed or resized to 1MB.
 * Images may be removed if they don't get at least 1 view every 3 months.