E-books, eBooks or ebooks? Remember that 'email' was hyphenated when it first entered the language; time will tell. We'll go with eBooks for the moment.
We need to distinguish eBooks (book-length documents designed to be read as a continuous unpaginated text sequence on a dedicated eReader) from online books, which might be conventional, paginated books, delivered electronically as PDFs or some other paginated format.
In regard to eBooks, the Amazon Kindle currently dominates the UK eBook market, which has so far largely featured fiction downloads that would not be indexed even in hard-copy. James Lamb has usefully reviewed the relationship of the current Kindle to indexes ('Kindle and the index', May 2011).
In the rush to convert hard-copy titles to ebooks, some publishers have uselessly reproduced the original indexes with meaningless page numbers, or converted page numbers to screen locations with inadequate precision, so the reader may not find the topic for several screenfuls beyond the indicated location. Many have simply retreated from the challenge of providing proper subject access at all, relying on search. More suitable solutions are available.
A key development was the International Digital Publishing Forum (IDPF) approval in May 2011 of the EPUB3 standard and the development by the IDPF Indexes Working Group (including representatives from The American Society for Indexing (ASI) and The Australian and New Zealand Society of Indexers (ANZSI)) of the EPUB3 Indexes Specification. This (June 2014) is awaiting approval by the IDPF. But this will just be the beginning as it will take time for publishers and reading device developers to implement the specification. Sanders Kleinfeld explains why in 'O'Reilly's journey to EPUB 3: Upgrading to EPUB 3 is not a trivial undertaking' - for even the most progressive of publishers, upgrades are challenging. For his most recent, upbeat, account which draws particular attention to the IWG's work on indexing in EPUB3, see 'Five reasons for optimism about the future of ebooks'. For those who are interested in trying to keep tabs on what's happening in the EPUB3 world, the Book Industry Study Group (BISG) has prepared a EPUB3 Support Grid showing what EPUB3 features are currently usable on which device, app, and reading system (Amazon, of course, doesn't tick any of the boxes). For a summary of the EPUB3 timeline and the Indexes Specification see 'Understanding the IDPF EPUB3 Indexes Specification'.