Yes, you can export your list and then import it back into the new server.
You do this by saving your list as a template (Go to Site Settings/Site libraries and lists/Customize list name you want to export)
When you get to this screen you can click on the "Save list as template". Fill out all the fields then make sure you click the 'Include Content' box and click 'OK'.
To import the list you go to your new server, and then go to Site Settings/List templates. You need to upload your saved template.
Go back to the Site Settings screen, and then go to your Site libraries and lists and then choose the 'Create new content' and choose the saved template. That should create a new list with all the content from the other server.
The only couple of caveats are these: You need to be the site admin to upload the template and create the list, and the list you are trying to create a template of must be under 10MB. There are ways to increase that size but I've never tried them.
Alternatively you can look at this blog posting for a pictorial view of how to do this:
http://grounding.co.za/blogs/neil/archive/2008/10/05/moving-a-list-with-content-between-sharepoint-servers.aspx