Generally speaking, no, you can't do it. There are some caveats to that. If you live in Sweden there are ways to do it. If you are talking about an anime (rather than a cartoon) that does not have a translation in the country you live in, there are some Japanese anime shops that allow for fan translations to exist. But in general, it would be copyright infringement unless you had an agreement with the company that owned the copyright. Almost any host would shut down the site as soon as they were informed about it. That prevents them from being held liable for your actions. Of course, they will probably let it run until they are approached about it.
I wonder if these Anime companies would ever agree to stream their videos online. lol. Doubtful, though it does give their Anime's more publicity, which in return is how many Anime's become popular enough to come to US/Canada.
There isn't much point to stream them until they have been subtitled or dubbed. There are a number of authorized fan-subs that can be downloaded. Most are not authorized, and even if they are, the fan-subs usually stop once the anime has a contract to be distributed in the US on tv/dvd.
Any special reason there are many big anime streaming sites that have not been shut down? Maybe a nicely worded disclaimer? Any ideas?
The reason is that many anime studios have chosen to allow them to continue because they act as a medium to get more fans. Japanese businesses tend to be much more long thinking than say the RIAA.