I think these topics are existing already numerous times, but hey, its fun to see if something is new.
Here are my mine which i use daily, seperated paid and free ones
Launcher pro plus, my fav. Launcher
Widgetlocker, great lockscreen.
Navigon, used it in my car before, now on my phone, very well organized navigation app.
Atakephone, best dialer i found.
Palmary weather, stunning graphics, lots of info, very accurate.
Tapatalk pro, for visiting this and some other forums.
Awesome drop, getting small files from your desktop to your mobile.
Tweetdeck, very clean twitter app
Open watch, for connecting my watch to my phone
Penetrate, getting codes from all thomson and speedtouch routers.
Chewitts dark theme for on my x10. Looks amazingly well.
Some dutch apps which are usefull, like buienradar, marktplaats, foongids, het verkeer, eredivisie, tvgids info etc.
Swype, best keyboard, got the apk from someone here, dont know if it is actually free...
Poweramp, stunning music player
Jorte, nice calender application
MIUI browser, damn slick and quik, can be downloaded here on xda, as the original is in Chinese but someone over here translated it to English
Callend Vibrate, just gives a little vibration when ending a call, very handy
Retro Calculator, great calculator which brings back memories from the old days at school.
Shootme (needs root) for shaking to make a screenshot
type fresh (needs root and busybox) to change fonts on your device
Zimly, for my videos
Kiss Ringtones, very nice ringtones, I like the classic ones the most.
Sent from my x10i using tapatalk and edited later by desktop ;)