So first of all, every space probe changes direction constantly due to the gravitational attraction of the Sun, and the planets and moons. For instance the Parker Solar probe orbits the Sun every few months, changing its motion (as seen, for example by an observer stationary with respect to the Sun and above its North pole) through a full 360 degrees each time. For most probes most of the time, this can be approximated by saying they are following an orbit around a planet (for instance the Mars Reconnaisance Orbiter, which orbits Mars) or the Sun (the Parker Solar probe). Let's call that its "main orbit".
When a probe passes near to another Moon or planet, it main orbit will be changed. This change can be quite dramatic, and this is exploited by mission designers to get the probes to where they want them. Parker Solar Probe makes many encouters with Venus, in order to adjust its orbit ever closer to the Sun. The Voyagers used their encounters with Jupiter and Saturn to speed and direct their courses into the outer system. Cassini used many encounters with Titan to adjust its trajectory, and so on.
For changed introduced "artificially" by firing rockets, they tend to be relatively small, because every kilo of rocket fuel that you have to carry is a kilo less for instruments etc. The biggest ones I am aware of are the braking burns needed for probes to be captured into orbit around their destination planet. For instance the Gallileo mission to Jupiter slowed by 630 $ms^{-1}$ to enter Jupiter orbit. Most of the time, a much smaller burn months ahead of time will achieve whatever goal is needed while using less fuel.
The obvious exception are ion drive probes, such as Dawn and Osiris-Rex. These can achieve quite large changes in trajectory over a period of years by a very small but prolonged thrust using only a very tiny amount of fuel. These changes can amount to several $km s^{-1}$ over a few years.
Rereading the question, are you perhaps asking about unplanned changes. Several people have mentioned secondary missions in the comments, which were not planned for (at least definitely) at launch time, but are added later, using whatever fuel is left. These almost always involve very small amounts of rocket thrust, because there is rarely much fuel available. New Horizons rerouted after Pluto but by a pretty small velocity change over a long time. Gallileo and Cassini both had mission extensions but did most of their maneuvering using the gravity of various moons. These might be called replanned.
Closer to what you maybe have in mind -- the Cassini probe trajectory had to be adjusted to overcome a flaw in the design of the telemetry link to the Huygens lander. I can't find any data on how big a change that was.
New Horizons had a contingency plan to change course near Pluto if any unexpected moons were discoverd as it approached, but this was not needed.
Another contender would be the International Space Station, which changes course slightly from time to time to avoid orbitting junk.