There have been several successful missions to short period comets. Some highlights:
The International Cometary Explorer in the late 1970s, an ESA/NASA collab and the first craft to visit a comet, 21P/Giacobini–Zinner. This was also the first Libration point mission of any kind, as it was initially parked at Sun-Earth L1. Indeed it was originally called the International Sun-Earth Explorer-3, and the cometary mission was something of an afterthought.
No fewer than 4 spacecraft had close encounters with Halley during its 1984/85 visit, Giotto being the closest encounter. Several other spacecraft made more distant observations.
Deep Space 1, whose primary target was an asteroid, was sent on after 19P/Borrelly, receiving the best images and science data from a comet ever recorded til that date. It was also a successful test of NASA’s ion rocketry.
Stardust was the first successful sample return mission from a comet (81P/Wild ). The encounter took place in 2004. Deep Impact impacted 9P/Tempel in 2005. Rosetta/Philae had a nearly 2 year encounter with 67P/Churyumov–Gerasimenko, including very close imaging and a landing by Philae.
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All this is well and good but so far there have been no encounters with long period comets. The reason is pretty obvious: long period comets are oncers. We can’t predict their arrival, we won’t see them again. Despite the name, a good chunk of them have no period at all, as they are on hyperbolic trajectories out of the solar system. Fortunately because of the surveys such as Pan-STARRS we do at least get a year or two of warning now but it’s not usually enough time to put together a mission from scratch.
It’s a darned shame because it is thought that as a population, LPCs will differ considerably from SPCs. They are fresh, mostly: sent straight from the Oord Cloud, not withered and depleted by multiple encounters with the sun. A close squiz would provide some extra information about the OC and the early solar system.
The Comet Interceptor
The ESA are building a craft called The Comet Interceptor specifically for the purpose of encountering a Long Period Comet. It will park at the L2 Sun-Earth Langrange point, with enough propellant for a few thousand km/s of delta-V in order to intercept, and speed-match, a carefully chosen LPC, in order to trail and observe it for several months at least. It will also send ahead two small specialised probes: one build by ESA, one by JAXA.
Launch is expected in 2028.
https://www.cometinterceptor.space/mission.html
https://www.cometinterceptor.space/uploads/1/2/3/7/123778284/comet_interceptor_executive_summary.pdf
http://www.esa.int/Science_Exploration/Space_Science/ESA_s_new_mission_to_intercept_a_comet
Although this dealie is meant for comets, I did think that it would be nice to have something like this on hand when ʻOumuamua flew through town three years ago. Unfortunately not all comets could be reached by this Interceptor, and you probably only get one shot: I would imagine that make the Go decision would be a bit nerve-wracking: what if you plump for some ho hum comet, and then the comet of the century comes by the following year?
