Q:

How do I know if it is safe to remove a wall?

When looking at a wall, how can I tell if I can safely remove it?

A:

Check if the wall is load-bearing

See that link for how to do this. 

Try to see if there are are any high-voltage lines in the wall 

Look for light switches, receptacles, lights, hard-wired smoke detector 
In some cases, a wire may run though the wall, but not be visible. This is very hard to determine, and takes sleuth work (look for wires entering the wall from floors above/below, and consider based on locations of other electrical if it's likely this wall is used to run wires). There are voltage detectors that MAY be able to detect the lines, but not guaranteed (though if they indicate, you know there's a line there for sure).

Check for low-voltage lines as well (cable, phone, internet, doorbell, HVAC, speakers). 

These are probably even harder to find than high-voltage lines unless there is something on the wall that gives it away. Accidentally cutting one of these is a pain, but not nearly as dangerous or life-threatening as a high-voltage line. 

Check for plumbing 

This can include hot/cold water, waste lines and vent lines. 
Waste plumbing works on gravity, and so it will usually take the shortest route. Find bathrooms/sinks and the main waste lines in the house, and see if this wall falls between them.
Supply plumbing is hard to detect unless there is a fixture on the wall. Requires some sleuth work. 

Check for air ducts 

Relatively easy to determine: if there is a vent on the wall or you can see duct work connecting to it (cavities inside walls are often used as vertical ducts)
Can be a bit harder to find if it's used as a riser to connect horizontal runs between two floors. If it's above/below the main duct run then it's possible. 
If you remove a wall without re-running vents, you may be cutting off the supply or return to an area of your house, which can reduce air quality and comfort.

Central vac pipes

Generally the rule is to try and avoid as many turns as possible, and avoid going up towards the vacuum. Same idea as finding waste lines: find the vacuum and the wall ports, and if this wall is in the most direct path between them it's likely to have lines. You may also be able to hear them, especially if you put your ear against the wall and have someone suck up a small pebble or something noisy (but that won't damage the vacuum). 

Gas lines

Pretty unlikely to find gas running through the middle of a wall (especially one you're considering tearing out) but it's still a possibility.
Again, if the wall is the most direct route between the gas source, and the appliance (consider: water heaters, furnace, oven, BBQ), it's possible 

In a commercial structure, the wall may be a fire wall (there will be doors on auto-closers separating this area from all others if this is the case - though check with your local fire department or building inspector). 

Of course, even if you are fairly confident there is nothing in the wall, don't just pull out the sawzall and tear through it - put some holes in it first to visually inspect for anything you might have missed. Most people will take all the drywall off at least one side before touching studs, as it gives that total check that everything is good to go. 

