What is the maximum number of partitions that can be made on a hard drive?
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).
From Technet: Reviewing Storage Limits: Local File Systems:
The number of disk drives you can use for each server is limited only by the available memory for FAT16, FAT32, NTFS, and UDF files systems.
So no there is no hard limit on Windows on the number of drivers. Drive letter are of course limited, since they stop at Z. But drives don't have to be given a drive letter - they can be mapped to a folder on another drive. From the same Technet article:
Mounted drives are useful when you want to add more storage to an existing volume without having to extend the volume. A mounted drive is a local volume attached to an empty folder on an NTFS volume. Mounted drives are not subject to the 26-drive limit imposed by drive letters, so you can use mounted drives to access more than 26 drives on your computer. For more information about mounted drives, including information about creating mounted drives on server clusters, see "Using NTFS mounted drives" in Help and Support Center for Windows Server 2003.