Pagination: Let the user choose how many items are shown per page?

Does it make sense to let the user chose how many items are shown per page? Or does it make sense under certain circumstances? When? When not?

This is how some big websites handle it:

  • Google: Used to be in advanced search, doesn't work with Google Instant
  • Bing: Can be set in preferences
  • Amazon: Nope
  • Ebay: Yes, looks like this:

Ebay items per page

My Impression is that this is a remnant from the old days when the number of items had a real impact on the loading time (so you would generally have it low and allow users with more bandwidth to set it higher). But many people I talked with want to keep the feature. Any thoughts? Pros and cons?