There are four blast lines, usually referred to as "bottom"/"lower", "left", "right", and "upper"/"ceiling" (alternatively, "north"/"south"/"east"/"west"). Brawl displays diagonal-pointing explosions if a character is KO'd in a corner, but this is only to improve the explosions' visibility.
Most stages have left and right blast lines which are far away from any ledges, and so cannot readily be walked into - exceptions to this include Mushroom Kingdom,Yoshi's Island and Green Hill Zone - and a lower blast line which is triggered by falling below the level of the screen. Some stages have full floors and walls that prevent access to certain blast lines, but they still exist, should a character be glitched through the stage.
The upper blast line is different from the others in that characters can freely pass it without being KO'd in most situations; characters can freely jump and attack above the blast line (the cause of the Luigi ladder). Characters are only KO'd off the top if they are standing on platforms that leave the stage or they are being propelled upwards by knockback, a broken shield, a thrown Screw Attack, or the Wario Waft. These characteristics do not apply in Super Smash Bros..
Characters KO'd via the upper blast line are either star KO'd or screen KO'd. There are a few exceptions to this however. In most battles in 1P Mode where the players fights a large team of opponents, the opponents are KO'd off the upper blast line as if it were any other blast line, instead of being star or screen KO'd. In Brawl, there's a glitch that causes characters who are KO'd over the upper blast line during the usage of a tether recovery to be KO'd with a simple colored blast. Additionally in Brawl, if a character is KO'd at the upper blast line while near the left or right blast line, they are KO'd as normal instead of star/screen KO'd.
The game's camera refuses to pan or zoom enough during gameplay to actually "see" the blast lines (although the lines themselves are invisible, as can be evidenced when the camera is rotated while pausing). When a character is between a blast line and the camera's view (or above the upper blast line without dying), they will appear in a bubble and slowly take damage. This is known as hoop damage.
In The Subspace Emissary's side-scrolling stages, the blast lines will not KO Player 2 if P2 is not hit by an enemy (similar to the upper blast line in normal gameplay). Player 2 will do an automatic Space Jump instead. Also, the upper blast line is stripped of its unique properties; characters don't need to be in knockback to be KO'd by it and don't fall into the background or foreground.
Items and projectiles that cross the blast lines are removed from play (except for, again, the upper blast line). A Smash Ball can freely cross blast lines until it chooses to leave.