What do I need to know to charge my American phone / razor / laptop in Europe? Do I need a simple converter, or do I need to take voltage in account?
If your phone charger, and your laptop are relatively new, they should work in Europe as-is, so you only need to bring the power plug adapter. I've never seen a single-voltage phone/laptop charger in more than ten years.
Razor however is different. Even if it says 110/240, it still might not work due to frequency difference (i.e. it will work in South Korea with 230V/60Hz, but might not work in France with 220V/50Hz). I had a Philips razor which was like that. Note that "razor outlets" provided in bathroom hotels rarely change frequency, only the voltage.
You should check what it says on the converter. My laptop charger, for example, says 110–240 V, 50–60 Hz. I have used it successfully in Europe and Canada (with the appropriate adapter where required. My phone charger says similar things (but I don’t have it on me right now).
My (American) PlayStation2 reads 110 V. This definitely needs a step-down converter.
There is some grey area in-between which I personally have never had to experience.
One hint, though: If whatever you’re using takes an AC input and internally turnes that into a DC output then it’s very, very likely that it’ll work (given it accepts the European 230 V at all). I believe all modern phones use a USB-type charger which is DC-based, so you should be fine with that (again assuming it can handle 230 V).