Add the compose key to your Xmodmap file with something like
keycode 134 = Multi_key
The compose key has it's own unicode symbol: ⎄, which I'll use in the following composition tables.
Accents
- ⎄`a à
 - ⎄'a á
 - ⎄^a â
 - ⎄ca ǎ
 - ⎄ba ă
 - ⎄oa å
 - ⎄!a ạ
 - ⎄.a ȧ
 - ⎄"a ä
 - ⎄~a ã
 - ⎄_a ā
 - ⎄;a ą
 - ⎄,c ç
 
Weird letters
- ⎄AE Æ
 - ⎄ae æ
 - ⎄ss ß
 - ⎄TH Þ
 - ⎄th þ
 
Currency
- ⎄=C €
 - ⎄|c ¢
 - ⎄-L £
 
Typography
- ⎄<< «
 - ⎄>> »
 - ⎄"< “
 - ⎄"> ”
 - ⎄'< ‘
 - ⎄'> ’
 - ⎄.. …
 - ⎄p! ¶
 - ⎄os §
 - ⎄?? ¿
 - ⎄!! ¡
 - ⎄--- — (em dash)
 - ⎄--. – (em dash)
 
Math
- ⎄oo °
 - ⎄^0 ⁰
 - ⎄^1 ¹
 - ⎄_1 ₁
 - ⎄12 ½
 - ⎄+- ±
 - ⎄xx ×
 - ⎄:- ÷
 - ⎄/o ø
 - ⎄mu µ
 
Business
- ⎄oc ©
 - ⎄or ®
 - ⎄tm ™
 
Emoticons
- ⎄:) ☺
 - ⎄:( ☹
 
As you can imagine, the list goes on and on. The compositing system depends on your application (see the Ubuntu wiki for Gnome notes), but if you're using the X Input Method (XIM), your compose table depends on your locale:
$ echo $LANG
en_US.UTF-8
$ grep $LANG\$ /usr/share/X11/locale/compose.dir
en_US.UTF-8/Compose             en_US.UTF-8
en_US.UTF-8/Compose:            en_US.UTF-8
$ less /usr/share/X11/locale/en_US.UTF-8/Compose
If you want to customize your compose keys, just add your own rules to
an ~/.XCompose file:
$ cat ~/.XCompose
include "%L"
<Multi_key> <h> <o> <m> <e> : "http://tremily.us/"  # Home page
Read Compose(5) for more information.  You may need to log out and
log back in (or use the newgrp trick) for your new ~/.XCompose
file to take effect.