I've only used Sharepoint very cursorily and that years ago, so my experience isn't the best or understanding complete.
As a first approximation: a Wiki.
Tools such as Atlassian's Trac and Jira (not themselves open sourced) offer a fair bit of the equivalent features.
For setting up Internet portals, a CMS such as Drupal or Wordpress could fit the bill.
One of the features of Sharepoint sites that I've seen is that they're used effectively to "hang" MS Office documents off of them -- as Office docs. This grates strongly with my preference for either HTML or PDF formats for documents, plus some markup style. I'm growing increasingly strongly partial to using either Markdown (for simple documents/pages) or LaTeX (for more complex ones) for document preparation. Yes, there's a touch of up-front training involved, but once you've crossed that bridge, the world opens up, and the basics can be gotten in an hour or so.
The document management pieces are actually something I'd like a solution for more generally, and it's a space that's hugely frustrating. There's zotero, a desktop application, there's git, there are a number of other tools, each of which effectively only address part of the larger picture.
You can write down the list of sharepoint features you need, and then find individual OSS projects that fill the gap. It's not a one-stop thing, but it doesn't have to be a deal breaker either.
SharePoint is a Jack of all trades, master of none so based on you requirements you have to choose the right tool most of which are OSS or at the very least non depended on Windows
Definitely true. A wiki provides a good chunk of what I've seen folks in academia use SP for but I've seen other companies use primarily the office-type features (calendar, contacts, etc). But if you setup a wiki along with something like Zimbra and that could provide most of what SP offers and some extras.
It really depends on your requirements. What is it that you need? Like any software SP is a tool, just like home improvement you don't go out buy a tool and than try to use it for what ever task is in front of you (you might end up with a screw driver while you really needed a hammer). So I could make a list of Document Management, Content Management, Intranet, etc software but the correct answer depends on your needs since there are lots of choose and all (some) have there own strong and weak points.
SP is a mesh up of several software suits slowly coming to getter, it is getting better every release. SP could also be the right choice depending in your needs. Mainly work group portals but those tend to fail (as in not being used) since most of the time there is no proper business case nor business processes in place to support the grand idea
If you respond with specific requirements I'll be glad to give you a rundown of options for each requirement, as well as good "package deals" of software that works well in concert.
