There have been four major US planetary probe events on (or scheduled for) 4th July. This compares to approximately a hundred "major events" for US planetary probes. At least one (Viking) was somewhat intentional - it had to be around early July and the 4th was deliberately picked - while others may fall into this category.
- Viking 1 landing, 1976 (delayed to July 20, itself nicely symbolic...)
- Mars Pathfinder landing, 1997
- Deep Impact flyby/impact, 2005
- Juno arrival, 2016.
Of these, the first was partly dictated by celestial mechanics and partly by date preference. Launch windows dictated an arrival at Mars around early July, and when the Viking mission planners sat down in 1970, they made the deliberate choice of 4th July out of a roughly one-week window:
Martin remarked that even if Viking had safely touched down on the Fourth of July, the landing "would have been lost among the Tall Ships," a reference to the publicity given the bicentennial parade of ships in New York harbor. That historic date had been chosen in 1970 after a preliminary trajectory analysis singled out the first week in July 1976 for a landing, but the Red Planet had not cooperated. The bicentennial was celebrated without a Viking on Mars.
(On Mars: Exploration of the Red Planet, ch. 10)
Pathfinder did not hang around in Mars orbit, and so the landing date was entirely dependent on the trajectory. Again, this would mean that it was probably an arbitrary selection of a target date in a longer window. I have not as yet been able to confirm that they did pick 4th July as a nicer date than 3rd or 5th, but this seems to have been generally assumed at the time.
Deep Impact - I've not been able to find anything on this one way or another. I suspect it was mostly coincidence - there cannot be much flexibility in the rendezvous window with a comet! The mission was originally planned to launch at the end of December 2004, and delayed two weeks until 12 January; a press kit for a proposed intermediate launch date of 8 January still expected a 4th July impact, but it seems this was driven by orbital and observation opportunities more than symbolism:
An impact on 4 July would not only be one day before the comet's perihelion, but would also mark an American national holiday. This solution roughly optimised several parameters, including lighting conditions and launcher performance, and the impact was scheduled for a one-hour window where it could be tracked by Deep Space Network antennas in both Australia and California, and the effect of the strike could be observed by the large telescopes in Hawaii and in space.
Juno - I've not been able to find anything either way as yet. I suspect it may fall into the category of "we have a broad window, pick an arbitrary date in the middle".
These are all American dates. It's worth considering the experience of other countries. The most obvious example in recent years is North Korea; more or less every launch attempt there is near an anniversary, if not on the specific day. Most prominently, the Kwangmyŏngsŏng-3 launch attempt was timed for what would have been Kim Il-Sung's hundredth birthday.
In the USSR, Soyuz 1 was scheduled to coincide with Lenin's birthday, and it's possible the resulting launch pressures may have contributed to the failure of that flight. I can't immediately find a reference to any other launches being timed around major anniversaries, but I'm sure there were some!