What are some good circuits for learning about capacitors?
I think the simplest are also the most informative.

Take a simple voltage divider built entirely of resistors:







simulate this circuit &ndash; Schematic created using CircuitLab

The voltage ( \$V_{Probe}\$)at the point marked "Probe" is given by:

$$V_{Probe} = V_1 \times \frac{R_2}{R_1+R_2} $$

Compare with the two variants possible using a resistor and a capacitor:







simulate this circuit

Voltage dividers work for impedances as well as for resistances.  

The impedance of a capacitor is given by:

$$ Z_C = \frac {1}{2 \pi f C}$$

Where:


\$C\$ is the capacitance in farads
\$f\$ is the frequency in hertz


You can put the impedance of a capacitor into the voltage divider formula, and calculate the voltage at "Probe" for various frequencies.  Compare calculated values with values you measure using your signal generator and your oscilloscope.

Can you tell which arrangement is typically referred to as high pass filter, and which arrangement is known as a low pass filter?