Yes. No. …well, maybe. Bolt-action rifles have only been around since 1824. However, they were the main infantry weapon for almost every army on the planet for nearly a century. They proved to have a relatively fast rate of fire coupled with almost infallible reliability. For military commanders who were used to dealing with muzzleloaders, this advancement was a godsend. The vast majority of modern hunting rifles today are bolt-actions along with a large percentage of military precision rifles. Despite their much sexier semi-automatic cousins, the bolt-action maintains a high level of popularity among all walks of shooters. As far as their obsolescence goes, I would compare them to a high-quality kitchen knife. Fancier electric knives can turn a Thanksgiving turkey into a plate of unrecognizable scraps in seconds, but the standard-size kitchen knife your grandmother used is perfectly suited for most of the jobs it will meet—just like the bolt-action.
Rate of Fire
We might as well start with the feature that made the bolt-action popular. In 20th century warfare, he who put the most lead downrange had a distinct advantage. Muzzleloaders and early breechloaders could not keep up with the simplistic yet effective bolt-action design. Ironically, that same rate of fire is what retired the bolt-action from regular infantry service. During the Second World War, semi-automatic weapons grew in popularity and reliability. As the major powers pushed semi-automatic and automatic designs to the front lines, the bolt-action rifles were simply outmatched. However, for snipers and other precision sharpshooters, rate of fire is not important. Accuracy plays the highest role and that requirement continues to this day. While there are extremely accurate semi-automatic rifles, the bolt-action continues to be the dominant choice for these dedicated precision weapons systems.
Bolt guns are extremely rugged. Their tough construction allows manufacturers to use extremely powerful cartridges for their designs without significantly increasing the size or weight of the weapon. For example, some of the most powerful elephant rifles are nearly the same weight as a typical deer rifle. Nearly every available cartridge has a bolt-action version, although some cartridges are more popular than others are. The best selling bolt actions today include the .30-06 Springfield, .270 Winchester, .308 Winchester, 7mm Remington Magnum, .243 Winchester and even the .223 Remington. In the surplus market, the Mosin Nagant variants continue to be one of the most common rifles sold in the United States. The powerful 7.62x54R cartridge is relatively accurate and inexpensive. The rifles themselves, being of varying age from both China and the former Soviet Union, range greatly in quality. However, the robust design makes a platform that will likely outlive us all. For a survival situation, a Mosin Nagant is on my personal list to have around. The plentiful ammunition comes in bulk and lasts indefinitely.
Because of their famed ruggedness, lower production cost, reliability and accuracy, bolt-action rifles will never be obsolete. There simply is no better way to operate the chamber manually on a rifle. While their days as standard infantry rifles are long retired, we will likely never find a better platform for precision shooting or game hunting.