I'll kick it off:

For me, it's IE for business, Mozilla for personal use and (usually) Chrome for Sparta and other MMO's, therefore the links below redirect mostly to Chrome extensions, although some of these are also available for other browsers, and even if not, similar extensions or clones are usually on offer:

1. "LightShot","GreenShot" and "ClipItGood" (for Chrome) ("SnagIt", a commercial product, as fall-back) to create screenshots; "qSnap" and "Nimbus" for multi-frame captures.
   
   
2. "Ookla" to keep track of bandwidth and latency (ping).
   
   
3. "Ears: Bass Boost" to change volume and equalise sound on specific browser tabs (SWOE has no volume control, so streaming audio or video in parallel tabs would be a challenge otherwise).
   
   
4. "zoomWheel" to zoom specific page URL's independent from browser zoom settings (such as different screen zooms for SWOE game and forum)
   
   
5. "Page Monitor" and "Spectator" to keep track of updated forum posts, since the SWOE forum does not support notifications.
   
   
6. "Google Drive" and "OneDrive" to store my screenshots and other related files.
   
   
7. "HTML-Online" (browser-based HTML editor) and "KompoZer" (offline HTML editor for Linux, Win, Mac) for writing longer posts with additional HTML tags.
   
   
8. "Google URL Shortener" to shorten links.
   
   
9. The "Google Translate" and "Grammarly" extensions for the obvious reasons.

Have I forgotten anything? Anyone have any suggestions, would be interesting to know.

Cheers,
P.