Yes, use the Workbook_Open() sub to call your macro, accessed by double-clicking on the 'Workbook' entry in your VB project explorer.
Workbook_Open() will run your macro, but it depends what you mean by "run continuously". If it's code that has to run when you do stuff in the spreadsheet, it will have to trap other events. Also, when the code runs, if it's long, Excel will stop processing and be unresponsive. If you want true background processing you need to run on another thread( by default Excel is single-threaded, except Excel 2002). If that's the case let me know and I can help out.
Use Workbook_Open() together with Do Events
Ivan