- Web clipping. Evernotes browser plugins are pretty darn good here.
- Notes with attachments (images, PDFs, etc.). Some of these are mixed-media notes, where text, images, and/or file attachments are mixed to create a comprehensive document about some topic. Others are "pure" attachments, e.g. "store this PDF where I can retrieve it by search".
- Note taking. This, in isolation, is the easiest.
- Note syncing, mobile and desktop. This gets a bit harder.
- Search. Let's be clear, this was the first and biggest killer feature of Evernote. Notebook and tag organization are important, but rather than just providing direct hierarchical/taxonomic organization, they're largely there to support search with user-defined search facets.
I'd also love good Markdown support – that's one of my most-wanted features from Evernote in the first place.