Users who purchase cheap, shared hosting packages are lumped together on the same server. This means that if any of the other users does anything with their hosting that modifies the operation of your server such as running an incorrectly programmed CRON job that continuously pulls resources away from the server, your site(s) will be effected by it. This may mean that your website could be offline for an undetermined amount of time due to the negligence 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 web hosting with a number of other users also means that your speed will be greatly diminished as you are sharing the overall bandwidth with every other user. If a user hosts a high traffic site, or a website that hosts lots of flash or video that takes a lot of bandwidth to load, your website will suffer the consequences. If you intend to create one of these sites yourself, you may not want to do it on shared web hosting.

If one of the users that shares your server has security flaws within their account there is a chance that any damage that can be done will be done to the entire server, not any of their sites alone. This will cause your websites to suffer any limited bandwidth or crashes that may result.

Cheap web hosting is an alright option if your intention is to host small content based sites and you don't stand to lose a lot of money from slow loading or downtimes. Just remember that cheap web hosting is not always synonymous with affordable webhosting.