According to information from the National Weather Service web page:

June 22nd, 1987
A rainfall total of 5.01 inches at the Buffalo Airport on the 22nd shattered the previous record for that date and set a new 24-hour rainfall record. The resulting flooding closed main arteries such as the N.Y.S Thruway, the Scajaquada Expressway and the Kensington Expressway. The gauge at Scajaquada creek recorded its highest reading ever - over 5 feet above flood stage. Cheektowaga, Depew and Lancaster suffered the brunt of the suburban flooding. In the city of Buffalo, flooding was reported throughout north Buffalo and the Black Rock section of the city. In north Buffalo, underground telephone cables became water logged and over 100 customers lost phone service. With innumerable streets closed, even normal short commutes home from work took hours.

A few years earlier we had our second highest 24-hour rainfall at Buffalo:

September 13-14 1979
The remnants of Tropical Storm Frederic brought record amounts of rainfall to western New York. Buffalo International Airport received 4.94 inches in a 24 hour period. The maximum recorded in the area was 7.10 inches at Holley in Orleans county. Frederic's heavy rains caused extensive flooding over much of western New York and the Buffalo metropolitan area. Most streams rose to above their flood stages. There were countless cases of basement flooding. Power was disrupted in some areas. Many roads were inundated. Schools and offices had to close. Damage to crops was very high, especially in Genesee county. Many property owners who live near streams were evacuated.

You can learn more about Buffalo's Weather History from the National Weather Service web page at: http://www.erh.noaa.gov/buf/wxhis.htm

Thanks to Tom Niziol, Meteorologist-in-Charge, National Weather Service, Buffalo and Don Paul, Chief Meterologist, WIVB-TV Channel 4 for contributing to IWEC's "Ask the Expert."