I was surprised to find that the Voyager spacecraft use tape to store data pending transmission to Earth. Amazing that they have enjoyed such a long operating life, given that they are mechanical devices and presumably consume a significant amount of power from an ever-diminishing supply. Have more modern space probe designs e.g. New Horizons continued to use tape, or have they switched to solid-state? This is in regard to storage needed for the largest amounts of data, presumably science data - images and such. Are there benefits to tape-based data storage aboard robotic spacecraft still favoring their use despite the drawbacks?
The Voyagers used tape because that was the state of the art in the 1970s. Rotating harddrives were available, but are less robust than tape drives (and would act like a gyroscope, complicating attitude changes). Non-volatile solid state storage was available at that time, but primitive: you had e.g. magnetic core memory. The Voyagers used this as RAM. A magnetic core memory with enough capacity to replace the tape unit may have been heavier than the tape unit.
Rotating harddisks were rarely used: this related question mentions one mission that used them.
More recent spacecraft like Cassini and New Horizons use Flash storage. The switch from tape to solid stage was done somewhere between the Galileo and Cassini missions. Galileo used a tape drive, which developed problems right around the Jupiter orbit insertion. For Cassini, a tape drive was considered but rejected:
A high-capacity, high-performance solid-state recorder (SSR) design was chosen for the main software and data-storage system of the Cassini spacecraft. The SSR design was selected rather than candidate moving-tape data-transport designs, which have a demonstrated lifetime. In contrast, the SSR design offers unlimited read and write opportunities. Additionally, the design of the SSR permits definition of up to 16 individual partitions, each controllable and accessible independently of the others. The Cassini SSR is designed to operate during intense radiation events, including passage through Saturn's trapped-proton belt, with indiscernible impact on data. Custom application- specific integrated circuits are used throughout the SSR.