Can I export to .stl without selecting items (export everything)? I've made some relatively simple models for 3D-printing which consist of many primitives (boxes etc). When I export to .stl only selected ones are put into it. Of'course I use B keyboard shortcut to select them all, but is there an option which will cause exporting everything without need to select them each time?
You cannot export .stl files without selecting at least one object.
My suggestion to you is dot not use box select objects by pressing 'B' 

To select all object just hit 'A' , to deselect all hit 'A' again