Note: most of these apps are free, at least for their basic versions (which are themselves very functional). Have at it!
App access
Circle launcher - I keep this on my home screen for all of the apps that I might like to keep close at hand. Very attractive and highly functional.
SwipePad - Set up a hotspot on your screen and you can call up a grid of 12 apps to access from anywhere on your phone. There are several paid-for extras (for example to expand the number of apps on the grid from 12), of which I've only bought the
AppLauncher, which lets you appoint the app drawer from one of the grid spots.
Tools
Airdroid - Many others have talked about it and it is a great app. Essentially performs a similar role to Samsung's "Kies Air", which lets you control various of your phone's functions from your computer over the wi-fi network.
aTimer - A grid of 15 configurable timers and stopwatches. You can label each individually too, if you like.
Calendar
aCalendar - A nice, clean and well-laid-out calendar app. I now use it in preference to HTC's built-in one. The developer seems to have put a lot continued work and thought into improving it.
Search
CloudMagic - A centralised search function to trawl through your Google and Twitter accounts. It works well, but doesn't support as many different account types as Greplin (but Greplin doesn't have an android app).
Evi - The best natural-language voice search app (think Siri-alike) I've used so far on Android. It had some initial server connection issues, but they have now been fixed. It doesn't perform voice actions, but it's worth a look.
Google Gesture Search -Allows you to search your phone for contacts, apps or bookmarks by drawing figures on the screen. You can activate it by turning the phone over and back again (although this drains the battery faster).
Location
Glympse - Location sharing done right. Share your location for a user-determined period of time or until you reach a set destination. Your location can be sent out to phone numbers, email addresses and even Facebook. Highly recommended.
Camera/gallery
Actionsnap - Lets you turn your phone into one of those Lomography cameras with multiple lenses that puts multiple images on the same frame. It makes for some pretty cool effects.
Pano - A great app for making panoramas - the stitching on this is excellent. My Sensation hasn't got an upgrade to ICS yet, so I don't know how this compares to the stock panorama utility on Android 4.0
Photo Calendar - I find scrolling through all of my photos to find the most recent ones annoying, so this organises your shots by day. Very useful and well presented.
Media
ReadItLater - I send so many things from either my Twitter feed or Google Reader to this. It saves article-style pages to your phone and to their website (which also has Firefox and Chrome add-ons available, so you can sync a bunch of different pages for later reading easily). It cleans up the layout, removes ads and gives you just what you want. Pretty much perfect.
Spool - Similar to ReaditLater (above), but for richer media like videos, etc. Not as fast, for obvious reasons, and the layout work isn't quite as good. However, the app is relatively new and they're still working on it, so it's worth a try.
Sensor Music Player - It allows you to use various of your phone's sensors to control your music's playback. Extremely cool.
Youtube Remote - Lets you control your Youtube viewing on your laptop or other screen from your phone or tablet.