This article is not exclusive to antique and collector cars but relates to all of the vehicles we drive. An ABC 20/20 news article described how tires that looked perfectly serviceable actually failed catastrophically. It was reported that useable tire life is only about six or seven years. Antique and collector cars tend to spend more time in the garage so the tires don’t wear out as much as they “time out”.
When you purchase tires, you need to know they haven't been sitting in a warehouse for several years. It is important to be able to decipher the date of manufacture code. This code is located on the sidewall near the rim. Note, it may be on the inside of the tire depending on how it was mounted.

There are two different dating methods. According to information provided by The Tire Rack:
Since 2000, the week and year the tire was produced has been provided by the last four digits of the Tire Identification Number with the 2 digits being used to identify the week immediately preceding the 2 digits used to identify the year. (for example DOT U2LL LMLR 5107 was made the 51st week of 2007.)
The Tire Identification Number for tires produced prior to 2000 was based on the assumption that tires would not be in service for ten years. While they were required to provide the same information as today’s tires, the week and year the tire was produced was contained in the last three digits. The 2 digits used to identify the week a tire was manufactured immediately preceded a single digit used to identify the year. (in this instance DOT EJ8J DFM 408 was made the 40th week of the 8th year of the decade.)
I read one account of a Porsche owner driving his fully restored ($100,000 plus) Speedster across a bridge when an old tire self-destructed. The owner momentarily lost control of the car and it swerved into the side of the bridge causing considerable damage to the car. Luckily, nobody was injured.
Fresh tires are relatively cheap insurance. How old are your tires?
Update - The following comments were provided by a local tire dealer. He provided some insight into the 20/20 video.
1. The tire tread shown on the side of the road were truck retreads - nothing to do with the issue.