Whether or not an accordion form is appropriate will depend on the purpose of the form.
Luke Wroblewski did some user testing with accordion forms and found that they didn't increase the number of people successfully completing the form (compared to single page or multi-page alternatives) but also noted that they didn't have a negative influence either.
...simply porting the same questions you have on one long web page or
across several web pages into an accordion form isn’t likely to
increase conversion... The flip side of this, of course, is that accordion forms aren't
likely to negatively influence conversion either.
The research did however find that users were considerably faster at completing accordion forms.
While completion speed may not be paramount for e-commerce, there are
plenty of other situations online where quickness matters. Online
auctions or exchanges come to mind, where the failure to act quickly
could result in a lost opportunity. Accordion forms just might fit the
bill in these situations.
Accordion forms are particularly useful when you want to provide users with a summary of what they've entered so far. Rather than having the form split over multiple pages with a summary page at the end, the accordion method builds the summary as each section is completed.