Information on this page:
Datasheets 653x
Known 6530 variants
6530 replacement for Commodore drives
6530 replacement in the KIM-1 clone and Micro-KIM
6530 replacement 6530 in KIM-1
6530 replacement in the Gottlieb soundsystems, the MIOT

The 6530, nick named RRIOT is quite a special IC in the 65xx family.
Timer, RAM (64 byte), ROM, I/O, Counter in one IC. It has a factory mask programmed ROM and the locations of its I/O and RAM and ROM are determined also in the factory.
The 6530 is found in among others the KIM-1 (6530 02, 6530 03), a Chess system with MicroChess by Peter Jennings (6530 24) and variants are used in Commodore disk drives.

The 6532 has no ROM and RAM size is 128 byte versus 64 in 6530. I/O and timer are functional identical to the 6530. The nickname is RIOT, and it is a general purpose I/O device in the 6502 family. Very popular in e.g. the Atari 2600, and many clone KIM-1’s.

There is a datasheet for an IC called the 6531, RRIOC for RAM ROM I/O Counter. I have never seen it in the wild though, but seen references to pinball machines using it.

A mistery 6530, 021 unknown sofar.

Datasheets

The 6530 was produced by most 6502 manufactures, from MOS Technology/Commodore SG to Rockwell and Synertek. All production datasheets that I have seen afaik identical, here I present some clean Rockwell datasheets. The first one is a preliminary MOS datasheet for the MCS6530, missing the ordering pages of the production version.
MOS Technology preliminary MCS6530
Rockwell 6530 RRIOT
6531 RRIOC
6532 RIOT
How to avoid timer interrupts during reset of the 6502

A CMOS version, the 65C32 exists, here a page from the 1983 Synertek Databook.

Known 6530 variants

6530-002 KIM-1 listing in KIM-1 Users manual
6530-003 KIM-1 listing in KIM-1 Users manual
6530-004 TIM Terminal Monitor, see the TIM page
6530-005 According this OSI appnote this is an unprogrammed version of the 6530 TIM. I have also seen ads for this part without further description of what this is.
It has the 16 I/O lines, 64 word RAM and the timer, which can generate an IRQ. One can assume the ROM is empty.

6530-006 Allied Leisure pinball version 1 (IC6)
6530-007 Allied Leisure pinball version 1 (IC3)
6530-008 Allied Leisure pinball version 1 (IC5)
6530-009 Allied Leisure pinball (IC5)
6530-010 Allied Leisure pinball (IC6)
6530-011 Allied Leisure / Fascination pinball (IC3)

6530-013 Used in the CBM 2040/3040/4040 disk drive DOS 1.0
6530-014 used in the Gottlieb System 1 sound boards
6530-016 Used in Gottlieb system 80/80A/80B sound boards

6530-024 Commodore CHESSmate (based upon Peter Jennings MicroChess)

6530-241 MIOT in pinball machines
6530-243 MIOT in pinball machines

Commodore diskdrives

901466-01 6530-??? DOS 1.0 Shugart SA390 2040, 3040 and 4040
901466-02 6530-028 DOS 1.2 Shugart SA390 2040, 3040 and 4040
901466-04 6530-034 DOS 2.0 DOS 2.1 Shugart SA390
901483-02 6530-036 DOS 2.5
901483-03 6530-038 DOS 2.5 Micropolis 1006-II (8050)
901483-04 6530-039 DOS 2.5 Tandon TM100-3M (8050)
901884-01 6530-040 DOS 2.7 Tandon TM100-3M (8050) Tandon TM100-4M (8250)
901885-01 6530-044 DOS 2.7 Micropolis ???
901885-04 6530-047 DOS 2.7 Micropolis 1006-II (8050) Micropolis 1006-IV (8250) Micropolis 1106-II (Safari, mit Garagentor, 8050) Micropolis 1106-IV (Safari, mit Garagentor, 8250)
901869-01 6530-048 DOS 2.7 M.P.I. 101SM (8050)M.P.I. 102?? (8250)
251256-02 6530-050 DOS 2.7 Matsushita JU-570-2 (8250LP)
251257-02A 2716 DOS 2.7 Matsushita JU-570 (SFD-1001) Matsushita JU-570-2 (SFD-1001)
251474-01B 2716 DOS 2.7 Matsushita JU-570-2 (8250LP)

Via an adapter board Commodore reused older 6530’s with new firmware by disabling the built in ROM and adding a 2716.
See Zimmers Commodore archive. Note that not just any 6530 can be used in this way, only the 6530’s from the Commodore diskdrives. A more general approach with a 6532 is described below.

A similar hack is replacing a non-functional KIM 6530 with a 6532, a 2716 and some glue logic: Gilbert Coville) http://gc.org/rc2011sc/ and http://gc.org/rc2012ww/

Micro-KIM

The Micro-KIM, see the whole story here,  is another variant of a KIM-1 with the original ROMS and 6532 instead of 6530.

See the complete circuit (version 2009!) here.