The requirements for Flight Data Recorders (FDRs) on airliners like the A320 is in 14 CFR 121. For a good summary of the requirements for flight recorders in various types of aircraft, see the NTSB FDR Handbook.
Depending on the certification date of the aircraft (14 CFR 121.343), the FDR must record between 6 and 17 parameters. Since engine parameters are included, this could be up to 23 different parameters on 4-engine aircraft. Newer Digital FDRs (DFDRs) must record at least 88 items (14 CFR 121.344). Some of these parameters are conditional, and some require multiple parameters, so the total will probably be more than 88 parameters. The NTSB report on the US Airways 1549 accident notes that the FDR recorded 178 parameters during the flight.
According to this page, tape-based DFDRs can record at 64 12-bit data words per second. Newer DFDRs using solid state recording can store up to 256 12-bit data words per second. This 256 words per second is also specified in the information on this FDR. It says it can record >100 hours at 64 words/second, which translates to about 35 MB total. The parameters are per DO-160C standard, which you have to pay to access.
Accident reports will generally include readouts from relevant parameters, to give an idea of the items that are recorded. There is a table here showing some parameters, the measurement range, and recording intervals. The interval is anywhere from 0.125 seconds to 4 seconds depending on the parameter.
Aircraft may also have a Quick Access Recorder (QAR), which records many parameters (over 2000). However, aircraft are not required to have one and the QAR is not required to survive an accident. Airlines use them for data to improve operations, and they can also be used in less severe crashes for analysis.