Recommendations here are (to the best of my knowledge) free unless otherwise stated.
Firefox Extensions
Tab-related:
Tabbrowser Preferences [kempez815]
Tab Mix Plus [Zathras]
IE Tab [herulach]
Navigation-related:
All-In-One Gestures [Russ]
Session Saver [hitman67]
Fasterfox [47 65 65 6b (Geek)]
Developer-related:
Web Developer [mike_w]
HTML Validator [mike_w]
MeasureIt [mike_w]
IEView [Paul Adams]
Download-related:
Down Them All (DtA) [Russ]
Filter-related:
AdBlock [kempez815]
Mail-related:
Gmail Notifier [kempez815]
AJAX Yahoo! Mail [Hans Voralberg]
Misc:
gTranslate [kempez815]
Toolbar Enhancements [iranu]
Split Screen [iranu]
Paste And Go [Hans Voralberg]
ForecastFox [Hans Voralberg]
FoxyTunes [skuzgib]
IE Plugins
Filter-related:
AdsFilter ($20, 30-day trial available) [Paul Adams]
Developer-related:
View In Firefox [Paul Adams]
HTML Source Explorer Bar [Paul Adams]
Misc:
Auto Refresher for IE (YRefresher) [Paul Adams]