What is the maximum number of partitions that can be made on a hard drive?

What is the maximum number of partitions we can make on hard disk in Windows?

If it is limited to some particular number, why can we assign all the letters C through Z to drives? If it is a special case, what's that?

On the legacy "MBR" partitioning scheme, you can have 4 primary partitions, or 3 primary partitions and one extended partition containing any number of logical partitions. While you can assign a drive letter to a partition, you can also map it as a folder in current versions of Windows, allowing more partitions, or use subst to mount it to a number.

The EFI specification mandates that a GUID Partition Table (GPT), which all modern operating systems support, is capable of containing a maximum of 128 partitions on any size hard disk. GPT is also required to boot from hard disk drives larger than 2 TB. This partitioning scheme is now widely used with UEFI being natively supported by practically all new computers.

In addition to native partitions, Windows and Linux also have something called a "logical volume manager", which can overlay dozens, if not hundreds of virtual partitions (logical volumes) on top of the 4 (MBR) or 128 (GPT) physical partitions. Logical volumes can be assigned drive letters or mountpoints in the same way as physical partitions. They can also be bootable if certain constraints are met.

It's also possible to have GPT-formatted disks on non-UEFI systems, and MBR disks on UEFI systems (with the exception of the boot disk).

On a disk using the traditional MBR format, the partition table has four slots. Each can hold a "primary" partition, or one can be used to create an "extended" partition which can contain any number of sub-partitions (often called "logical drives"). Extended partitions are basically a workaround for the small size of the MBR partition table, and there are limitations on what they can be used for. (For example, the Windows bootloader must be on a primary partition.)

The newer GPT disk format supports many more partitions — technically unlimited, I think, but operating systems impose a limit of 128. These are all "primary" partitions (to use the MBR terminology).