Yeah those are a few I guess.
There's also three official test carts which each offer a variety of tests.
-------------------------Container--------------------------
File: SNES Aging Test Program (J) (R1.2).SFC
---------------------Internal ROM Info----------------------
Name: _____________________ Company: Unlicensed
Header: None Bank: HiROM
Interleaved: None ROM: 1 Mb
Type: Normal SRAM: 0 Kb
Expansion: None Battery: None
Country: Japan Video: NTSC
ROM Speed: 200ns (SlowROM) Revision: 1.0
Checksum: Corrupt, Bad 0x1B1C Game Code: None
---------------------------Hashes---------------------------
CRC32: 55938E4E
--------------------------Database--------------------------
Name: SNES Aging Test Program
Country: Japan Revision: 1.2
Port 1: Gamepad Port 2: Gamepad
Genre 1: Test Cartridge Genre 2: None
-------------------------Container--------------------------
File: SNES Controller Test Program (J).SFC
---------------------Internal ROM Info----------------------
Name: _____________________ Company: Unlicensed
Header: None Bank: HiROM
Interleaved: None ROM: 1 Mb
Type: Normal SRAM: 0 Kb
Expansion: None Battery: None
Country: Japan Video: NTSC
ROM Speed: 200ns (SlowROM) Revision: 1.0
Checksum: Corrupt, Bad 0xB9CC Game Code: None
---------------------------Hashes---------------------------
CRC32: EDF7EBB9
--------------------------Database--------------------------
Name: SNES Controller Test Program
Country: Japan Revision: 1.0
Port 1: Gamepad Port 2: Gamepad
Genre 1: Test Cartridge Genre 2: None
-------------------------Container--------------------------
File: SNES Test Program (U).SFC
---------------------Internal ROM Info----------------------
Name: _____________________ Company: Unlicensed
Header: None Bank: LoROM
Interleaved: None ROM: 5 Mb
Type: Normal SRAM: 0 Kb
Expansion: None Battery: None
Country: Japan Video: NTSC
ROM Speed: 200ns (SlowROM) Revision: 1.0
Checksum: Corrupt, Bad 0xE8BC Game Code: None
---------------------------Hashes---------------------------
CRC32: 71DB3BC5
--------------------------Database--------------------------
Name: SNES Test Program
Country: USA Revision: 1.0
Port 1: Gamepad Port 2: Gamepad
Genre 1: Test Cartridge Genre 2: None
Mega Man X2 and 3 also have several tests performed when you press B on controller two on game load.
Far East of Eden Zero, Momotarou Dentetsu Happy, and Super Power League 4 also have tests on first game load.
Although between all these, it's not that many tests, and hardly too much in-depth like some of the other emulation pages offer. However, it is something.