can I feed my arduino UNO with a 5V cellphone USB power supply ? Since the arduino board doesn't regulate the 5V from the USB input, is a cellphone power supply sufficiently regulated ?
Yes. USB is a standard. You can even use 5V power packs for portable gizmos.
Caution: Ken Shirrif have a good post about non-original USB chargers and its perils. (A dozen USB chargers in the lab: Apple is very good, but not quite the best). Read them and learn a lot.
I only use the original charger that comes with the cell or tablet (and that usually last longer that the cell or tablet that it comes with). I don't trust any third party USB charger or car adapter after Ken's analysis
It is a USB (1.0 & 2.0) requirement that a USB Host power lines are 5 volts and can supply up to 500mA. Here is a USB power standards table from wikipedia.org.
If your Arduino project pulls more, then the 5 volt level may drop. That is to say, for more than 500mA you will need to consult the power pack specifications.
In general terms yes, the output of a USB power adaptor for a mobile phone will be suitably stabilised.
Most phones have the ability to monitor the voltage and adjust the charging current depending on the voltage they see. If the voltage drops below, say 4.5V, they will reduce the current they draw until it rises back above that threshold (as can be seen if you use a 1A cable on a 2A charger, the phone will throttle the current to within the 1A range since the cable imposes too high a voltage drop).
For this reason it is important that power adaptors put out the correct voltage otherwise mobile phones wouldn't be able to work properly with them.
Cheap imported USB power adaptors often fall far below proper safety standards, though, so you should use a proper branded one (Apple, Samsung, etc) from a reputable dealer, not something for $4 off eBay. Those cheap ones are a serious safety hazard and can cause electric shocks and fires.