This is one of the biggest problem with power strips (surge protectors)...

Overload!

The average person does not think about how much power each device is drawing, or how much the system can handle, they just see an open outlet and plug stuff in. If they can't find an open outlet... Oh yeah! they make adapters for that! I mean they sell the adapters, so they must be safe... Right?

If your power strips look like this (or worse), you better at least be checking the batteries in that smoke alarm (which is hopefully not plugged into this power strip too).

If you are using the power strip (or extension cord) properly (one plug per outlet, no adapters, no daisy chaining) and you inspect the power strip for damage (wear & tear) regularly, you should not have much to fear.

Another thing to look at when using a power strip or extension cord, is the size of the wire and the voltage and amperage ratings. If you are using things like electric heaters, power tools, vacuums, etc., make sure the wire (extension cord/power strip) is the proper size to handle the above average load of these types of devices. Overloaded wire can heat up quickly and cause a fire.

Basically if you use common sense, inspect the cables for obvious damage and/or wear & tear regularly, and use the cables for their intended purpose, you should have no problems using extension cords and/or power strips.

Here is some interesting stuff from The Office of Compliance about Power Strips and Dangerous Daisy Chains.

Problems:

OSHA regulations require that conductors and electrical equipment be used in accordance with the conditions under which they are approved by a recognized testing organization (29 CFR 1910.303(a)). Most power strips are approved for providing power to a maximum of four or six individual items; however, when multiple power strips are interconnected, the one directly connected to the building outlet is often supplying power to far more than the approved number. This electrical current overload can result in a fire or can cause a circuit breaker to trip, deenergizing computers and other equipment throughout the area. The risk is magnified when another outlet in the same wall or floor receptacle is also overloaded in a similar fashion. When other outlets on the same circuit are also overloaded, the risk increases.

Extension cords are sometimes used to energize power strips in locations far from outlets. Because electrical resistance increases with increased power cord length, interconnecting cords increases the total resistance and resultant heat generation. This creates an additional risk of equipment failure and fire, particularly when paper and other combustible materials are in contact with the wires. Additionally, OSHA’s regulations allow extension cords to be used only as temporary wiring for up to 90 days. Unfortunately,once in place, extension cords tend to become permanent wiring and a fire hazard.

Solutions:

Several safe solutions exist. In many cases, a power strip energized by an extension cord or another power strip can simply be replaced by a power strip with a power cord of adequate length to reach an outlet. Other times, use of a power strip that is better able to accommodate bulkier transformer plugs solves the problem. Several factors should be considered when selecting an appropriate surge protector. Since models vary in the amount of current that they are rated to safely carry, it is important to consider the amperage requirements of the devices to be energized. Models vary in length of power cord, typically ranging from three to 15 feet. Choose one whose length is most appropriate for reaching the intended room outlet. Avoid having too much excess cord, and make sure the surge protector is set on its base. Some have swivel plugs which makes them easier to connect to the outlet, and helps to protect the plug and cord from damage. Check each surge protector to make sure it is in good condition for use.

Only power strips equipped with internal fuses are acceptable as permanent wiring. Those lacking these fuses are equivalent to extension cords, and therefore may not be used as permanent wiring. When a power strip is installed, care must be taken to ensure that it is not suspended in mid-air by its power cord or cords plugged into it, resulting in excessive stress on electrical connections.

The National Electrical Code (NEC) has a whole article devoted to flexible cords and cables, one of the more applicable sections in this case would be 400.8.

2008 National Electrical Code

ARTICLE 400 Flexible Cords and Cables

400.8 Uses Not Permitted. Unless specifically permitted in 400.7, flexible cords and cables shall not be used for the following:
(1) As a substitute for the fixed wiring of a structure
(2) Where run through holes in walls, structural ceilings, suspended ceilings, dropped ceilings, or floors
(3) Where run through doorways, windows, or similar openings
(4) Where attached to building surfaces
*Exception to (4): Flexible cord and cable shall be permitted to be attached to building surfaces in accordance with the provisions of 368.56(B)**
(5) Where concealed by walls, floors, or ceilings or located above suspended or dropped ceilings
(6) Where installed in raceways, except as otherwise permitted in this Code
(7) Where subject to physical damage

*368.56(B) Cord and Cable Assemblies. Suitable cord and cable assemblies approved for extra-hard usage or hard usage and listed bus drop cable shall be permitted as branches from busways for the connection of portable equipment or the connection of stationary equipment to facilitate their interchange in accordance with 400.7 and 400.8 and the following conditions:
(1) The cord or cable shall be attached to the building by an approved means.
(2) The length of the cord or cable from a busway plug-in device to a suitable tension take-up support device shall not exceed 1.8 m (6 ft).
(3) The cord and cable shall be installed as a vertical riser from the tension take-up support device to the equipment served.
(4) Strain relief cable grips shall be provided for the cord or cable at the busway plug-in device and equipment terminations.

400.8(1) As a substitute for the fixed wiring of a structure.

400.8(2) Where run through holes in walls, structural ceilings, suspended ceilings, dropped ceilings, or floors.

400.8(3) Where run through doorways, windows, or similar openings.

400.8(4) Where attached to building surfaces.

400.8(5) Where concealed by walls, floors, or ceilings or located above suspended or dropped ceilings.

400.8(6) Where installed in raceways, except as otherwise permitted in this Code

400.8(7) Where subject to physical damage

Get a heavy stand

Growing up, my dad had a traditional stand that looks something like this:

That works for smaller trees as long as you can be sure that nobody (such as a child or pet) will disturb it. That's not at all a given. Remember that trees have extensive root systems that keep them grounded during windy periods and so it's important to get a stand that can simulate the parts of the tree that have been cut off. For that reason, I'm a proponent of a heavier stand such as this one made of cast iron:

There's something to be said for the simplicity of a really heavy, wide stand that will hold your tree firmly in place. I've been told plastic stands are sturdier than they look when they are weighted with water. They have the additional advantage of holding a gallon of water or more, which means you won't risk a dried out tree. In some ways it doesn't matter what the stand looks like since you can always cover it with a tree skirt. (And my wife insists on it even though I like the way our stand looks.)

Placing the tree in the stand

One thing I've tried is to set the tree up before removing the twine that holds the branches in place. This is a mistake for two reasons:

1. The balance of the tree changes when the branches are fully deployed. A tree that stands straight when wrapped can sometimes end up leaning when unwrapped.

2. My wife always wants me to rotate the tree so that the best side is facing into the room. Once the tree is secure, you don't want to mess with the balance by trying to move or rotate it.

For the sake of getting a good balance, I also think it's a mistake to attach the stand before putting the tree upright. Or rather, you're going to need to readjust it anyway and it probably won't buy you anything—especially if you have a heavy stand.

Attaching the tree to the stand

Here's where my stand fails me. It attaches to the tree with three screws. Three is the absolute minimum number of points need to hold a trunk in place and it doesn't seem to be enough. If I try to adjust one side, the tree starts falling over and I need help holding it up. (My father's stand had the same problem, but image searches show most of the traditional design have 4 screws plus a ring to hold the truck more securely.)

This year I hit on a solution that's so simple I can't figure out how it didn't occur to me before: I put 2x4 scraps between the screws and the trunk. This has the advantage of spreading the side pressure to a larger area and also makes adjustments easier since the bolts don't screw into the trunk itself. For added security, I packing in extra scraps of wood to brace the tree now that I have it secured to the stand.

Looking around, I see that newer designs use two levels of screws or even "hug" the trunk with a pedal operated cable. I don't have any experience with these designs, but if the stand is heavy enough (see above) they are probably improvements over the three-screw stand that I'm using.

Consider a guyline

Here in California, we are encouraged to secure everything in case of earthquake. Given the excitement of the season, I like to secure our tree in case of childquake. It's a bit of a hassle, but in years past, I've been glad to have a bit of safety from tree fall when its balance shifted due to watering and decorations. It need not be an eyesore either—the line might be secured to a hook in the wall behind the tree.

I've used monofilament fishing line to attach our tree to a hook in the ceiling. Since the fishing line is designed to be invisible (or close to it) in water, most people won't see it. A bonus advantage is that you know what your line is rated and can estimate how many strands will suffice. If you do fish in the summer, its a good idea to replace your line between fishing seasons to avoid tangles, so this is a perfect opportunity.