I have never played a game using a modern digital clock. I always used an analog clock; the ones equipped with a "flag" (a Dutch invention) that falls to indicate the moment the player's time has expired. A major drawback of the mechanical clocks was the accuracy of when the flag fell. Also additional time cannot easily be added for more complex time controls. But, in those days things were simpler; there weren't any complex time controls like exist today. At the beginning of the game you added an extra minute to the time (this was probably unofficial, but the idea was to make up for any mechanical problems or something like that) and when the flag fell, the game was lost. Simple.
In 1973, to address the issues with analog clocks, Bruce Cheney, a Cornell University Electrical Engineering student and chess player, created the first digital chess clock as a project for an undergraduate EE course. It was crude compared to the products on the market many years later. For example, the display was done with red LEDs. LEDs require significant power, and as a result, the clock had to be plugged into a wall outlet. The high cost of LEDs at the time meant that only one set of digits could be displayed, that of the player whose turn it was to move. This meant that each player's time had to be multiplexed to the display when their time was running.
A chess clock that was patented in 1975 was developed by Joseph Meshi and became the first commercially available digital chess clock.
Digital clocks resulted in a wave of experimentation with more varied time controls, some quite complex. One particularly notable development was proposed by Bobby Fischer, who in 1988 filed for U.S. Patent 4,884,255 (awarded in 1989) for a new type of digital chess clock. Fischer's digital clock gave each player a fixed period of time at the start of the game and then added a small amount after each move. In this way, the players would never be desperately short of time, but games could also be completed more quickly, doing away with the need for adjournments.
On March 10, 1994, a patent application was filed by inventors Frank A. Camaratta, Jr. of Huntsville, AL, and Wllliam Goichberg of Salisbury Mills, NY for a game timer which employed a delay feature. It provided a delay between the time the button is pressed and the time that the clock actually begins to count down. The benefit is, it reduces the likelihood that a player with an advantage will lose solely because of the expiration of time.
To be honest, I prefer the simple analog clock. All these new digital clocks and time controls give me a headache just thinking about them. That said, when it come to encounters between the world's elite players, I do like the idea of eliminating adjournments. It seems wrong to decide a game between the best players in the world based on blitz games, but I suppose it's no more wrong than losing in a time scramble or adjourning and letting a gaggle of seconds analyze all night. At least the results in blitz are the results of a players own thoughts.
Anyway, there was something about being in a tournament room and hearing the quiet ticking of a whole bunch of chess clocks that was relaxing. I'd rather use any of these clocks
Carolus Chess has an interesting history of the chess clock.
Dorland's Antique Set and Clocks is another interesting site.