This is a list of extensions I find most useful.
Tracker is an efficient and fast desktop search engine. Open Source desktop search experienced a painful set-back when faux Open Source advocates ignorantly crusading against the Mono project bludgeoned the reputation of the Beagle project based on a few bugs experienced in early releases [as if every project and product doesn't have those]. Tracker stepped in to replace Beagle, and being implemented in C, avoided the ire of the trolls [or at least that set of trolls]. It has taken a l-o-n-g time for Tracker to match Beagle's level of awesome, but that day has arrived. And to put this amazing little search engine work for you is the Tracker Search extension. This extension adds search results derived from all your data to the search feature of Shell's overview mode; you can see applications, recent items, and the top matches from your data all in one dynamic view. This extension is like having your own personal secretary with a degree in library science - and who doesn't want that?
Disable Hot Corners
GNOME Shell features hot corners so that it can claim to support the hip new thing known as "gestures". Gestures are an awful idea and impede usability. This extension disables hot corners - win!. If you have a keyboard you can get to overview mode using either Alt-F1 or the Windows key; what could be faster? Nothing. If you do not have a keyboard you almost certainly are not doing anything productive anyway - go outside, get some exercise, make some friends who don't live in their mother's basement.
Zeitgeist is the activity hub of the Open Source desktop. It correlates and records your activity and the data you access. In conjunction with Tracker and the Tracker Search this provides a nearly full-fledged secretarial service. Often times I can resume what I ended working on yesterday directly from the GNOME Activity Journal. This extension adds all that knowledge and context to Shell's overview mode.
Frequently I just need to run something, or check something, and I to do so I need a terminal window. This extension puts an icon on Shell's top bar that with a single click always gives me a shiny new shell. Simple.
Advanced Settings in UserMenu
GNOME hackers haven't quite settled on where settings belong. It appears that between all the various work environments that may just be an eternal question. And people have strong opinions about it. So GNOME Shell provides "System Settings" in the drop down menu. But... a lot of settings aren't there. Including the ability to enable and disable extensions. This extension just adds an "Advanced Settings" option which shortcuts to the gnome-tweak-tool where numerous [officially unsupported] settings can be tweaked (hence the name). In gnome-tweak-tool it is also possible to enable and disable extensions. This extension just makes it faster to get to the tool. Once you have things the way you really want you won't use it much, but getting to that point you'll possibly be searching for and running gnome-tweak-tool on a regular basis.
Dash to Dock
This extension makes the dash [the dashboard for launching favorite applications] a bit more like a dock or toolbar. The dash will stick around, even when not in overview, until a window presses it out of the way. Sometimes it is a bit too sticky but most of the time it works as expected. The best part of the modified behavior is that every time you navigate to a new [empty] workspace the dash is ready and waiting for you to summon some applications.
This great little extension drops a new drop-down menu into the top bar of the Shell from which you can create, via one-click, a new SSH session from a predefined lists of hosts. And there is not froggin' about in a configuration file to setup the hosts - the extension provides a handy configuration dialog to add and remove host entries. It even integrates with the GNOME Terminal profiles so that you can select what profile you'd like for each SSH host entry. This is a must-have for the beleaguered system adminstrator.