Note: Some of these shortcuts have been remapped for my own convenience (Preferences->Keymap). These are Mac shortcuts, just use the Windows/Linux equivalent of the Cmd/Option/Ctrl/Del keys.
####Search, Go to, Navigation ####
Cmd + P - Search file
Cmd + Shift + O - Search everywhere
(I swapped the above two recently because I use Cmd + P to search for files most of the time).
Cmd + O - Open Class
Cmd + R - Go to Symbol
Cmd + N - Generate things
Cmd + L - Go to Line
Cmd + Up - Navigate Folders (goodbye sidebar)
Cmd + Shift + F - Search for text in a folder or entire project
Cmd + Shift + Del - Go to last edit location (Thanks Laracasts)
Cmd + J - Insert Live Template (snippet)
Option + Enter - Show intention actions
Ctrl + T - Refactor This
**Cmd + § ** - Jump from different PHPStorm windows/projects
Cmd + Shift + A - The shortcut to all shortcuts