Voltage Controlled Current Source integrated circuit? Exists?
Since you haven't specified output impedance, accuracy, or much anything else except as few components as possible, this is what you want:



This makes use of the propoerties of a bipolar transistor where its collector current is largely not dependent on collector voltage, and the B-E drop is reasonably fixed.  The voltage on the emitter will be close to Vin + 700 mV.  The power voltage minus that will be across the resistor.  That voltage divided by the resistor value will be the current thru the resistor, which is close to the collector current.

Let's say you want the 0-350 mA output current range controlled by a 3.5 V range of voltage.  In that case, R1 would be 100 &Omega;, and the control voltage range would be PWR - 700 mV to PWR - 4.2 V.

This isn't what I would call a "precision" current source, but it is actually good enough for many real applications.  It can be made more precise by putting a opamp around it to more accurately control the voltage across the resistor.  Once you have that, you can use a PFET instead of a bipolar transistor because the feedback will compensate for the G-S voltage not being as fixed as the B-E voltage of a bipolar transistor.  The advantage of a FET is that the drain current equals the source current (and therefore the resistor current), whereas with a bipolar the collector current is the emitter current minus the small base current.  However, since your primary goal is simplicity without mention of other parameters, such more complicated topologies would just be overkill.