I'd like to add a trash icon to the Gnome 3 favorites vertical bar on the left of the desktop.
Just make your own launcher e.g.
[Desktop Entry] Version=1.0 Type=Application Name=Trash Can Viewer Comment=Because I Can! Exec=gvfs-open trash:/// Icon=user-trash Terminal=false Categories=GNOME;
place it1 in
~/.local/share/applications) if you intent it to be user-specific or in
/usr/share/applications) if you want it to be available to all users; then, while in overview mode, click on the Show Applications button on the dash (or use Super+A), find the trash icon and just drag it to dash (favourites).
1: Note that on some setups the desktop file has to be "marked as trusted" (either double click it and Mark As Trusted or make it executable and add
#!/usr/bin/env xdg-open at the top of the file).