depends on your hosting package but most likely yes, your hosting environment will support a number of server side frameworks such as php, asp.net. do a google search for “email contact form” and there will be many tutorials and info to wade through.
If you plan to install server site scripts for your website you could setup a ticket management system so you can target messages by topics/departments and also ask other custom questions about the submitter (his messenger id, website url, how did he find you… ).