Cheap, shared hosting packages are placed in large numbers on the same server. Therefore when one of the other users does something with their hosting that modifies the operation of your server such as running a faulty CRON job that continuously pulls resources away from the server, your site(s) and everyone elses will be effected by it. This may mean that your websites could be offline for an undetermined amount of time due to the ignorance of just one user. Since there are often dozens of users on a single shared server, the odds of a possible crash are against you.
Sharing a web hosting server also means sharing the overall bandwidth available to the server. If one of the other users hosts a high traffic site, or a website that contains lots of video or flash that takes a long time to load, your website will suffer as a result. If it was your intention to host one of these sites yourself, you probably don't want to do it on shared web hosting.
If one of the users that shares your hosting has security flaws within their site there is a good chance that any damage that may be done will be done to the server itself, not any of their sites alone. The resulting crashes and limited bandwidth will be suffered by your site(s) as well.
Cheap web hosting is an okay option if your intention is to host several small, text based content sites and you are not worried about possible downtime or slow loading times. Just remember that cheap, shared hosting is not always comparable to affordable webhosting.