The following hot keys work in all windows of the program:
Enter - press the active button. In the main program window this hot key executes a file if it has been completely downloaded, otherwise opens the download information window;
Esc - close the window;
Ctrl+Alt+S - start all uncompleted downloads;
Ctrl+Alt+P - pause all started downloads;
F1 - show the help system.

Main program window
Insert/Ctrl+N - add URL;
Ctrl+S - start the selected download(s);
Ctrl+Shift - lets you to force a download to be started from the control panel;
Ctrl+Shift+S (can be changed in the program settings) - force download to start;
Ctrl+P - pause the selected download(s);
Ctrl+C - copy the URL of the selected download or download group;
Ctrl+Shift+C - copy the URL and description of the selected download. Also, it works in the "Add Download" and "Download Information" windows;
F4 - open/close category list;
F5 - open/close download log;
F7 - open FTP Explorer;
Ctrl+H - open download history;
Alt+"up arrow" and Alt+"down arrow" - move the selected download(s)/categories along the list;
Alt+Ctrl+Up Arrow and Alt+Ctrl+Down Arrow - move to the top and the bottom of the list respectively;
Alt+Enter - open the "Download properties"/"Category properties" window;
Del - delete the selected download(s)/categories from the list;
Ctrl/Shift+Del/mouse click - delete the selected downloads from the list along with the corresponding downloaded files;
Shift+double click - open the folder to which the download is saved;
Ctrl+R - mark as "read";
Ctrl+U - mark as "unread";
Ctrl+A - select all downloads in the list;
Ctrl+M - check the MD5 sum of a downloaded file;
Ctrl+D - copy MD5 sum to clipboard;
Ctrl+1 - check the SHA1 sum of a downloaded file;
Ctrl+2 - check the SHA256 sum of a downloaded file;
Ctrl+F - search in the download list;
F3 - continue search in the download list with the specified parameters;
Ctrl+F3 or Shift+Ctrl+F - open the file search window.

Add/edit URL window
Ctrl+R - Allows you to edit the refferer field manually;

Ctrl+Enter/click - download later;
Shift+Enter/click - schedule and start download;
Alt+Enter/click - add with high priority.
( i ) You can use any combination of these keys, i.e. Alt+Ctrl+Shift+Enter.

Add multiple URLs window
Alt+click - select (deselect) all files with the same extension.

IDA-browser window
F3 or Ctrl+F - open the file search window;
Ctrl+F4 - close the browser window.

Internet Explorer (If enabled in Integration options)
Alt+mouse clickF3 - send download to IDA;
Ctrl+mouse click - open download with browser.

Global Windows shortcuts
These keyboard shortcuts work in all Windows applications allowing you to control IDA without switching to IDA application. These shortcuts can be set up in Options->Shortcuts. By default IDA uses the following shortcuts:
Shift+Ctrl+O - open/close IDA;
Shift+Ctrl+P - temporary start/stop all downloads;
Shift+Ctrl+H - set maximum download speed;
Shift+Ctrl+L - set minimum download speed.