I want to set up a couple of different websites. Do I need a hosting account for each of them?
Up until as recently as a couple of years ago the answer would have been yes. However, the high level of competition amongst hosting companies (particularly in the US), has lead to various innovations becoming the industry standard. Nowadays nearly all hosting accounts will give you the option of hosting a number of websites with the one account.
The advantages to this are obvious. Most host companies offer a huge amount of diskspace and bandwidth for their accounts (safe in the knowledge that 90% of their customers never get close to using a fraction of it), meaning you can comfortably host a number of small to medium sized websites on the one account. Your visitors won't have any obvious indication that your sites are linked, and you have, generally, one single administration point.
The disadvantages? Well, you're putting all your eggs into one basket, as they say. If your hosting account server has a problem, it's a problem for all your sites (though when choosing a host you should ensure they have a 99%uptime guarantee - meaning if the server goes down for longer than 1% of the hours in any given month that you'll get some kind of refund).
Another problem can be in terms of website statistics. Depending upon how your host sets up the account, you may find that server stats only refer directly to your main domain (i.e the domain that you used to open the account). This may or may not be a problem, depending upon your needs. Server stats, while not 100% accurate, are an extremely important tool for search engine optimisation. They give you info about how many people visit your site, what pages they look at etc. It's always worth checking with a potential hosting company whether your stats package will cover each domain separately.