Is a sharepoint 2007 webpart likely to work on 2010 without any modification? If not, what are the main areas that would require modification?
Most likely it will migrate without issue. If you are using the ASP.NET namespace to inherit from for the web part (as opposed to the SharePoint one) you will be fine.
The SharePoint OM hasn't dramatically changed either. A lot of the changes have be on how you can access the data (Client Object models), workflow changes, etc.
Of course, test :)
Have a look at my series of posts about porting a SharePoint 2007 WSPBuilder Project to SharePoint 2010.
Most of your code will probably work as expected. Please notice that because of stricter adherence to W3C standards you may experience some UI issues (that really depends on how strict you were in the first place, IE quirks would not work).
Also pay attention to the changes in the SSP functionality, well, for once, there is no SSP any more. Namespaces having to do with user profiles and such have been changed and your code could be broken now