How to make a multiline cursor without using a mouse in Sublime text 3?

Standard key bindings not work for me(Ubuntu 16.4 and Win 10), but after redefining works good! To redefine default key bindings use (Preferences->Key Bindings)

{ "keys": ["alt+shift+down"], "command": "select_lines", "args":{"forward": true} } will add cursor below, { "keys": ["alt+shift+up"], "command": "select_lines", "args": {"forward": false} } will add cursor above.

You can use Middle mouse button for this as well.

Click & Hold Middle mouse button and drag up and down

Yes, there is. Using Shift↓ or Shift↑, select the lines you want multiple cursors on. Next, hit CtrlShiftL (CommandShiftL on macOS) to split the selection into lines. Finally, hitting ← will put the cursors at the beginning of the lines, while → will put them at the end.

Edit

There is also another, quicker way (thanks to minitech) - CtrlAlt↑/↓ will create multiple cursors without having to do selections first, and you can place the cursors anywhere in the line you wish. However, on Windows these key combos may be mapped to changing the screen orientation. To change this, hit CtrlAltF12 to open the Intel control panel, click Options, and either remap the screen orientation hotkeys, or click Off on the left side to disable all of them.