Users who purchase cheap, shared hosting packages are lumped together on the same server. This means that if any of the other users does something with their hosting that modifies the operation of the 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 could mean that your websites could be offline for an undetermined amount of time due to the negligence of a single user. Since there are often dozens of users on a single shared server, the odds of a possible crash are against you.
Sharing the server with a number of users also means that the amount of available bandwidth is split between all users. If a user hosts a high traffic site, or a website that contains lots of flash or video 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 will not 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 chance that any damage that may be done will be done to the server itself, not that user's sites or account alone. This will cause your websites to suffer any crashes or limited bandwidth that may result.
Cheap web hosting is an alright option if your plan is to host several small, text based content sites and slow loading or downtimes will not affect your plans. Just keep in mind that cheap, shared hosting is not always synonymous with affordable webhosting.
