Do power outlet splitters decrease power for each deviced connected to them?

If split, all plugs will get the same access to "power".

Your outlets themselves are splitters: in general several outlets share a run of wire back to the power source. The external "spliter" is no different, it just provides more connection points to the same electrical circuit.

However: the total circuit capacity is neither increased nor decreased by a splitter. Devices "draw" current based on their needs: for example a motor generally draws more power when loaded than when spinning freely. If the total draw exceeds the circuit capacity, a protective device will trip. The protective device is usually set at 15 or 20 amps in a residential circuit.

Extra connections or total extension cord length can have a minor effect: a long thin cord with a heavy load can heat up, using up some of the electricity in transmission. In effect the wire becomes an electric resistance heater. This effect is usually negligible.

There is two kinds of power. There is "pressure" and there is "amount".

The pressure is unchanged, so you can run the same devices and they will work exactly like before.

But the amount of electricity is also unchanged, but, now it has to be shared. Since usually devices don't need the full amount available to them (they only take what they need) this works.

But if you had 3 devices that all took the maximum amount of electricity possible then it wouldn't work - there's not enough.

The thing I call "amount" is really called "watts". The maximum watts from a single outlet is 1,800. (1,500 is more realistic.) (Note: On a technical level it's really "amps", or "electrical current", but I don't want to make this confusing.)

So add up the wattage from each device (it's printed on them) and make sure not to go over.

Electricity doesn't work like that. At any given moment, there is an infinite amount of "power" available. However, as electricity flows to the device, heat is generated due to resistance along the pathway. If the pathway gets too hot, it will be damaged. Because of this, we use breakers and fuses to prevent the pathways from overheating.

Each device connected to the system will be able to use as much electricity as it wants. But once the pathway gets too hot, the breaker will trip or the fuse will blow (or the pathway will be destroyed).

Cautions I would add are:

I have had cases where people use a splitter, add say a 6 or 8 outlet power strip extension, then fill that powering tv, sterio and computer related equipment, etc. Often they forget that other outlets in the same room or even other rooms may be using the same circuit. They plug in a hair dryer or other heavy power using devices on top of other things they have plugged into other outlets and the fuse or circuitbreaker blows or overheats the wiring.

You have to keep aware of what you are using on the same circuit. Its good to check plugs and power cord wires at all outlets on the same circuit to make sure they are not getting hot. You can also carefully check the fuse or circuitbreaker to see if they are getting hot (if any are you may need to rearrange your devices or use a different circuit for some of your devices).

Power draw of devices can be an important issues if they have large motor driven eqwipment. I had someone who had a refrigerator on the same circuit as an air conditioner. At times that the refrigerator motor started at the same time as the air conditioner motor, lights would dim & the TV picture would act up. This can eventually damage the motors or other equipment.

When motors start they take more power & compete for the power they need. In this case sharing power is more critcal. If at all possible its better to run heavier motor driven equipment on separate circuits (usually dedicated circuits designed for their usage are best). If you have devices like large copy machines, printers or shredders, etc. put them on separate outlets or circuits &/or use them one at a time if you can't put them on separate circuits -these shoud be directly plugged into outlets or use heavy-duty extension cords, as much as possible only for the distance needed to reach an outlet. Don"t use a 15 ft extension cord if you only need one 3 ft long, especially for heavier motor driven equipment.

@tester: I only posted this as an answer b/c I can't post comments yet. I don't have enough points but there was no sense rewriting what is already in correct answers.

No, devices don't get less power when using a splitter, each device plugged into the splitter will get its required power. The only time this won't happen is if you overload a circuit.

     A common misconception is that one outlet gives a set amount of power. If this were the case, the more items you plug into an outlet the less power each item gets. So what actually happens when you plug more devices into an outlet using an outlet splitter? The outlet provides more power! But there is a limit. This is best explained using an example.

How does your outlet know how much power to provide:
     Say there is a single to triple outlet splitter plugged into a wall outlet in your living room. Lets also say you have three lamps which use 120 Watt light bulbs which operate at 120 Volts and draw 1 Amp each. Lets also say you want to power all three at the same time using this splitter. A single bulb draws 120 Volts and 1 Amp, equating to a power usage of 120 Watts. If you plugged all three lamps into the splitter at the same time, each bulb would still draw its needed voltage and current. Because the bulbs are hooked up in parallel, the total Voltage drop your livingroom outlet experiences is the same while the currents gets added together. This results in a combined total of 120 Volts at 3 Amps, equating to a power usage of 360 Watts. Although the 360 Watts is "split" between the bulbs, this does not reduce the needed power (120 Watts) each one of the bulbs gets.
     If the livingroom outlet is protected by a 15 Amp fuse, then there is no problem because the combined current draw is only 3 Amps. But if you are charging equipment with a combined total current draw of more than 15 Amps, the fuse will blow. No need to worry though, fuses are designed to fail so the equipment you plug into the outlet won't be damaged. Most household equipment doesn't use anywhere near 15 Amps, so this is usually a non-issue.

TL,DR; You get 120 volts always. Adding more devices makes the circuit deliver more AMPERES.

Within operational parameters, your wall outlet will deliver 120 volts. Every regular outlet in your house will deliver this voltage. You can think of this as analogous to water pressure at the bottom of an enormous tank - no matter how many taps you have at the bottom, the pressure will be the same at all of them.

For reasons of safety, your outlet is fused in the panel (actually the entire circuit, but keep it simple) at 15 amps. Amperes is the measure of current, or the amount of electrical charge flowing through the circuit. This is analogous to the amount of water flowing out of a tap. (The word CURRENT is even borrowed from fluid dynamics).

Lastly, we have Resistance, which is the load you put on the circuit. It is measured in Ohms. The problem with resistance is that it is counter-intuitive when talking about parallel circuits (which we are). Because if I add another device, I'm adding more resistors, and total resistance should go UP. But it doesn't. When you add a device in parallel, you are adding an additional conductive path to the circuit. In light of this, lets talk about 1/R, the inverse of resistance. This quantity is called conductance, and it allows us to think of adding another path, rather than adding another resistor. (And this holds up beautifully with our water metaphor -- Adding a high resistance hose to and existing system means MORE water will flow, not less.) The symbol for conductance is G and the units are siemens (S) -- After the German Electronics Firm.

NOTE: Resistance values are completely made up. Actual values are in the 250 Ohm range

So, your phone charger has a resistance of 30 Ohms. According to ohms law (I=V/R), that means the current in your circuit is 120/30 = 4 Amps. Thinking in terms of conductance, Ohm's law becomes I = VG, which is I = 120 *(1/30) = 4 Amps. (same thing).

Now lets add a second phone to the circuit. The total Conductance will be 1/30 + 1/30 = .06666... We now have two paths for the current to flow, so our conductance has doubled. 120 * (0.0666...) = 8 amps. And so has our current.

Add another, and the conductance will be 3 * (1/30) or 0.1 and the current will be 12 amps.

Add another, and the conductance will be 4 * (1/30) or 0.1333333, current will be 16 amps.

At this point we are dangerously overloading the circuit. The wires in your wall will start getting hot, and there is a potential of fire. This is why your breaker will flip -- to protect the wiring from overheating.

In reality, your circuit is already split. One breaker in your panel typically feeds several outlets and lights. That's why if you were to vacuum, Iron, make coffee and toast in your living room, you'd likely blow the breaker. The conductance would go through the roof and current would follow.

I work for an internet company and I do see the effect of old surge protectors, if they are older than 5 years they usually cause a lot of resistance that does effect the router, but more importantly what else is plugged in with routers makes a huge difference how a powerstrip wears and tears, avoid plugging in lamps, printers, speakers, heaters, scanners, toasters, anything that heats or cools, it is usually the power draw of other devices that stress out the low power DC devices that are usually wireless/internet capable. most devices last longer and work better if plugged in this way, I have 25 years of experience in saving money this way.

You can imagine the splitter like a buffet.
The food is not split but everyone can take the amount needed from the buffet. If 2 people join the buffet, no one gets less food. The only time there is a problem is if there are too many people or the people are too hungry.
The same applies for the outlet splitter. If there are too many devices then it's possible that they exceed the power limit of one outlet but usually, all devices get the same power as usual.