Is it important that power supplies for LED strips have limited current?
Sometimes a misunderstanding about current/power pops up: it's not because a power supply can deliver say 10A that it also will do so. It's the load which determines how much current will flow. In this example any current the load wants is OK, as long as it's less than 10A. 1mA: OK. 100mA: OK. 1A: OK, 100A: not OK, because more than what the power supply can deliver. It will deliver the maximum (10A), and the load has to see what it can do with it. Since it asks for more the voltage will probably drop, and the device will not function properly anymore.  

So stay below the maximum your supply can deliver and you'll be fine.  

edit: Q &amp; A  

Q the question is how much does the LED strip act like a resistor, no?
A More or less, but not quite. LEDs don't act as normal resistors; they will always force a fixed voltage drop over them. If your LEDs are 1.4V then 5 of them in series will cause a 7V drop. If you have a 12V supply then the remaining 5V will be over a resistor you always place in series with the LEDs. That resistor is required because it limits the current, and you use Ohm's Law to determine its value. Suppose the LEDs need 20mA. That's the current through the LEDs and therefore also through the resistor, and the voltage drop over the resistor is 5V. Then, according to Ohm's Law \$R = \frac{V}{I} = \frac{5V}{20mA} = 250\Omega\$. That's how you can decide yourself how much current will flow by choosing the right resistor value.