GtkRadiant/The Clipper
The clipper tool is one of th most important tools, and being able to use it properly will make things a lot easier for you. Like all other tools, the clipper tool must be activated to be able to use it. To activate it, press X or click the 
button in the toolbar. When the tool is selected, select at least one brush, then click on two different spots (you may also click 3 but that will be covered later). A line will appear between the two spots. Then press CTRL+ENTER to switch between the two parts and ENTER to accept the cut or SHIFT+ENTER to accept the cut and keep both parts of the brush. Then press X or click the button again to turn off the clipper. Now deselect everything and you will see that the brush is not cut into two different pieces. Of course you can keep clipping on a brush before you turn off the clipper to make it look like you want, you can also use the clipper again.