Although it's not particularly clear, a neat feature of xtightvnc
is the ability to modify the pop-up menu that appears when you press
F8 to send arbitrary keystrokes.

The trick is overriding some of the X11 resources of the file. If
you have a look in /etc/X11/app-defaults/Vncviewer (make sure
you have a recent
package) you can see the default keybindings for the popup menu,
which are a good template. Assuming you want to keep them all, you
can add your own buttons by starting at button 9 and re-defining the
total button count in your ~/.Xresources:

xtightvncviewer*popupButtonCount: 11

xtightvncviewer*popup*button9.label: Alt-F1
xtightvncviewer*popup*button9.translations: #override\n\
<Btn1Down>,<Btn1Up>: \
SendRFBEvent(keydown,Alt_L) \
SendRFBEvent(keydown,F1) \
SendRFBEvent(keyup, F1) \
SendRFBEvent(keyup, Alt_L)

xtightvncviewer*popup*button10.label: Alt-F2
xtightvncviewer*popup*button10.translations: #override\n\
<Btn1Down>,<Btn1Up>: \
SendRFBEvent(keydown,Alt_L) \
SendRFBEvent(keydown,F2) \
SendRFBEvent(keyup, F2) \
SendRFBEvent(keyup, Alt_L)

xtightvncviewer*popup*button11.label: Alt-F12
xtightvncviewer*popup*button11.translations: #override\n\
<Btn1Down>,<Btn1Up>: \
SendRFBEvent(keydown,Alt_L) \
SendRFBEvent(keydown,F12) \

Make sure you merge this with xrdb -merge ~/.Xresources if
you don't want to bother logging out and in. This way I can easily
send Alt-F1, etc. through to the other side; useful for things like
switching virtual terminals in VMware workstation running remotely. I
imagine if you were insane you could do all sorts of other tricks
too!