CPK is an archive format used in the Persona series from Persona 3 Portable onwards. It was developed by CRI Middleware and is the successor of CVM. Usually, most game data except for executables is stored in compressed CPK archives.
CriPakGUI can open and extract most CPK files easily with its very user friendly interface. You can download it from here.
aluigi's file extractor QuickBMS has scripts in .bms format for CPK archives. Run quickbms.exe, select cpk.bms, and then select your CPK file. It will automatically extract the contents to the directory of your choosing.
CRI Packed File Maker
While the Mod Compendium is an easier to use alternative, CRI Packed File Maker creates CPK files from an extracted directory and can be used to view file information such as data alignment, number of files, and compression modes. Use the commandline tool provided in the program's folder (cpkmakec.exe) to make a new CPK using the CSV file from the thread.
cpkmakec.exe Usage: cpkmakec.exe data.csv data.cpk -dir=UNPACKEDFILESDIRECTORY -align=2048 -mode=FILENAME -view
To make your own CSV file for a different CPK, use CpkFilelistDumper.exe (also found in the thread).
CpkFilelistDumper.exe Usage: CpkFilelistDumper.exe data.cpk
CriFsLib Extractor GUI
Also known as CriFsLib, CriFsV2Lib and CriFsLib.GUI; a tool developed by Sewer56 with the intent of being user-friendly, minimalistic, self contained (no dependencies) and high performance. All you need is to drag and drop your CPK, right click and extract. It doesn't support repacking since the status quo doesn't require it for modding. The tool is available for download here.