Under the normal DOS partitioning scheme, up to four primary partitions or three primary partitions and one extended partition containing as many logical partitions as you want. (In practice this is limited by the size of the disk.)
Whether the disk is IDE, SATA, SCSI, whatever is irrelevant.
Another viable alternative on Linux distros to place an entire disk (or partition) under LVM control as a PV. Once that is assigned to a VG, you can create as many LVs as you want (not sure what the limit is, but it's HUGE). LVs take the role of "partition" in the general case.