Are you looking for something to use or something to contribute to or what?
If you really care about popular and trendy, get some real data e.g. from http://sourceforge.net/softwaremap/ and be surprised that the most popular of the past week are a package of Microsoft Fonts and an ERP, Accounting and CRM app. The most popular of all time are eMule and Azaureus file sharing and Sourceforge.net itself and the Crystal Space 3D SDK.
In fact the most webby looking one in the lists seems to be PHPMyAdmin, of all things.
edit: naturally, 5 minutes after I wrote this we decided to go live with it http://news.ycombinator.com/edit?id=1069047
List seems to change fast.
"PostBooks ERP, accounting, CRM by xTuple - CRM, ERP, Accounting"
It shouldn't change fast if it is based on 7 days of traffic, but who knows what SForge does internally.
(It's not really popular or trendy, but I think it's cool and I like it a lot.)
Haskell is really taking off, both in terms of compiler improvements and in the size of the community and available libraries. I'm using it for several projects now.
MagLev, LuaJIT, Unladen Swallow, and V8 (again) are all exciting because they're bringing modern dynamic language VMs closer to Java-like (and sometimes even C-like) speeds.
Android - my phone runs an open source OS, I can install software on it without an app store, and it can run SSH, Python, and Lua. Sweet!
Not having to even worry about whether or not a library I want to use is blocking is a really useful feature.
It's built on top of EventMachine - Ruby equivalent of Twisted.
Also there's a growing, awesome community.
Clojure/Lisp - I've had a Lisp like language on my languages-to-learn to-do list for long
Redis - Looks like an excellent NoSQL DB to begin learning this new concept with.
"noSQL": Riak, MongoDB, Redis, (I think the "new-ness" has worn off CouchDB")
Trendy: node.js, ruby on rails, django, lift
*Really any "web framework that promises to make development easier"
want to play with openframeworks and cvtypes, but haven't had time
Edit: To the persons who downvoted me. I was not being sarcastic. I use stuff from the Jakarta project on a daily basis.
{project}
regardless of whether I like or dislike the project, and equally upvote everyone who posted
{project because .. reasons or thoughts or justifications or content which took some time to write ..}
But hardly anyone seems to have bothered, and I feel mean now so I've stopped. :/
Learn the exact copy on write semantics of forking (What happens to file handles? Threads? How does the OS know a paged needs to be copied?), copy two file descriptors with splice, put something in shared memory, move messages over an IPC queue.
It's used by millions of people all over the world (http://moodle.org/stats/) and is helping to make education more accessible.
Drupal
jQuery (included in Drupal)
Xdebug
EtherPad
Adium
Miro
Quicksilver
ClyppanMerging of the two largest open-source .NET math libraries...should be an excellent library when it's complete.
Ruby equivalent of Tornado?
Those are the essentials - I'm sure there is more.
squeak