In menu:

File
Ctrl+O	Open	Open file
Ctrl+S	Save	Save modifications
Shift+Ctrl+S	Save all	Save all modified files
Ctrl+F4	Close	Close current document
Shift+Ctrl+F4	Close all	Close all documents
Alt+F4	Quit	Quit HAPedit
Edit
Ctrl+Z	Undo	Undo last modification
Shift+Ctrl+Z	Redo	Revert last undo
Ctrl+X	Cut	Cut selected text
Ctrl+C	Copy	Copy selected text
Ctrl+V	Paste	Paste text from clipboard
Shift+Ctrl+V	Special Paste	Apply special filter to clipboard text (Configure the filter by selecting Ctrl+D => Filter/Paste).
Ctrl+A	Select all	Select all text
Ctrl+E	Edit tag	Edit html tag under cursor
Shift+Ctrl+E	Select tag	Select tag from <tag> to </tag>
Search
Ctrl+F	Find	Search for string in document, all open documents or in multiple project files
Ctrl+F3	Find Selected	Search for next occurence of selected text
F3	Find Next	Find next of last string search for
Ctrl+R	Replace...	Replace text in document(s) or in project files
Ctrl+G	Goto line...	Move cursor to specified line
Actions
Ctrl+Q	Query String	Associate Query String with current document for http requests
Alt+F12	SQL Console...	Display SQL console for executing requests
Shift+F2	"Compiled" code	Display "compiled" code of current document
Ctrl+F2	HTML Validator	Display html parsed code of current document
Ctrl+F9	Compile code	Compile dynamic page code
Actions -> Image
Ctrl+I	Insert image...	Select image to insert
Ctrl+Enter	Preview image...	Preview image under cursor
Actions -> Link
Ctrl+L	Create link	Create link (<a href="">)
Shift+Ctrl+L	Create anchor	Create anchor (<a name="">)
Ctrl+Enter	Open link under cursor	Open link under cursor (local file)
Actions -> Text
Ctrl+Alt+F (a)	Font	Insert tag <font>
Ctrl+Alt+P (a)	Paragraph	Paragraph <p>
Ctrl+Alt+B (a)	Block quote	Insert block quote <blockquote>
Ctrl+Alt+D (a)	Align text	Align selected text with tag <div>
Shift+Ctrl+G	Bold	Set selected text in bold
Shift+Ctrl+I	Italic	Set selected text in italic
Shift+Ctrl+U	Underline	Set selected text underlined
Shift+Ctrl+F	Apply filter	Apply user filter to selected text (Configure the filter by selecting Ctrl+D => Filter/Paste)
Shift+Ctrl+M	Convert to lowercase	Convert selected text to lowercase
Ctrl+Alt+M (a)	Convert to uppercase	Convert selected text to uppercase
Shift+Ctrl+S	Convert spaces	Convert spaces to
Shift+Ctrl+P	Convert to asp or php	Replace " character in selected text with \" (PHP) or "" (ASP)
Ctrl+H	Insert Html string...	Insert string and convert special chars to HTML entities
Shift+Ctrl+H	Convert to HTML	Convert special chars to HTML entities in selected text
Actions -> Special
Ctrl+P	Add list items...	Define list style to insert
Ctrl+B	Insert tag...	Insert tag or enclose selected text within specified tag
Shift+Ctrl+B	Insert tag ASP or PHP	Insert <% %> or <? ?>
Ctrl+N	Add invisible char	Add non-breaking space
Ctrl+M	Add carriage return	Add tag <br>
Shift+Ctrl+C	Insert comment	Insert Html comment
Ctrl+Alt+C (a)	Add HTML color	Add numeric HTML color from color palette
Project
Ctrl+Alt+O (a)	Open...	Open project files
Ctrl+F10	Projects list	Display projects list
Shift+F10	Folder File	Open project explorer handling folder of current file
Display -> Views
F2	Documents	Switch to panel "Documents" to edit some code
F6	Images	Switch to panel "Images" to explore code images
F7	Links	Switch to panel "Links" to explore code links
F8	Properties	Switch to panel "Properties"
F9	Page	Launch default browser to view the page
F10	Folders	Switch to panel "Folders" to manage internal folders
F11	Information	Switch to panel "Information"
Display
F12	Organize...	Organize opened documents
Ctrl+F11	Clip Library	Display or mask a dockable windows with useful clips
Ctrl+D	Languages	Select from complete drop-down lists of native functions, methods and properties in ASP, PHP, VBScript, ADOB, CSS-1 to insert in document at the cursor.
F5	Refresh	Refresh active panel view
Ctrl+K	Show blocks	Highlight dynamic code blocks
Shift+Ctrl+K	Brace-Matching	Highlight brace block '{}', '()' or '[]'
Help
F1	Summary	Help summary
Shift+F1	Index	Help index
Ctrl+F1	Contextual Help	Html or php help for current tag or function

In editor:

Code
Ctrl+J	Show Code Template (drop-down list of macros)
Ctrl+Space	Show Code Completion drop-down.
Shift+Ctrl+Space	Show Code Hint (syntax help for PHP function parameters)
Move
Ctrl+Right	One word to the right
Ctrl+Left	One word to the left
Ctrl+PgUp	Top of screen
Ctrl+PgDn	Bottom of screen
Alt+Right	Next document
Alt+Left	Previous document
Alt+Up	Beginning of current code block: '()', '{}' ou '[]'
Alt+Down	End of current code block: '()', '{}' ou '[]'
Delete
Ctrl+T	Delete word to the right of cursor
Ctrl+BkSp	Delete word to the left of cursor
Ctrl+Y	Delete current line (entire line).
Shift+Ctrl+Y	Delete to end of line (from cursor right).
Ctrl+Del	Delete text within 2 HTML tags.
Shift+Ctrl+Del	Delete the both HTML tags (open/close) around the text.
Misc
Escape	Cancel selection / Close Code Completion
F4	Toggle text selection mode (Normal/Column/Line)
From Shift+Ctrl+0 to Shift+Ctrl+9	Place Bookmark
From Ctrl+0 to Ctrl+9	Go to Bookmark

Note :
(a) Extended shortcuts: can be deactivated in general Options.

Realised with Tom L.'s help.