I need a hosting package that will allow me to host multiple sites/domain names. Do hosts do this? Anything specific I should look for?
Hosts that use the cPanel control panel will often advertise the ability to host additional domains as "addon domains". It's a common feature to be able to host multiple domains on a shared hosting account. Many, if not most such accounts, come allow an "unlimited" number of domains to be hosted. Obviously, "unlimited" is more of a marketing word, it's not really infinite. At some point the number of domains in itself could become an issue for the server, and the "resources abuse" clause will come into effect.
Anyway, if you want to be extra safe, contact the host about the particular package that you're interested in, and they should be able to clarify the situation for you.
Most major hosts these days offer a reseller programme too, always worth checking out depending on your needs.
Some hosts do allow multiple (or unlimited) domains to be hosted on an account. Other hosts charge a small additional monthly fee to host additional domain names. My host allows the hosting of as many add-on domains as a client wants without any additional fee. It's a nice feature because you can register a new domain name and try a new idea without having to pay extra to the hosting company.
Does having several domain names on one host account affect seo/search engine ranking, etc?
parked domains on cPanel server mostly used to divert traffic on another (main) domain. Use of multiple parked domains can be use for seo purpose. You can refer to http://docs.cpanel.net/twiki/bin/view/11_30/CpanelDocs/ParkedDomains
Most of the hosting companies offer various plans. Usually the lowest plan supports only ONE domain (in most cases) and the higher plans support more domains. You need to check how many add-on domains are supported. Further, if you want to build database sites then you will also need to see how many databases does it offer and the "space" provided per database. Some have like a limit of 50mb to 200mb and some offer higher limits. If you plan to create a database driven site, then you need to consider that too.