The martian atmosphere is 6 mbar. How do we know this? Which probe(s) had a barometer on board to measure this?
TFB's answer is correct that both Vikings made barometric measurements (and it is what the question asked for!), but it's worth noting that the atmosphere had been measured before surface instruments were available, and seems to have got pretty close to the current value.
In 1965, Mariner 4 carried out radio-occultation experiments, where the probe's signal was measured as it passed through the atmosphere before being eclipsed by Mars. These were used to calculate an estimated surface pressure of 4.1 to 7.0 mbar, depending on the model used for the composition of the atmosphere. Model II was for 80-100% CO2 with the balance N2/Ar (we now know it to be ~95% CO2), and gave a surface pressure of 4.1-6.2 mbar. There was a caveat to these measurements in that they suspected the signal had been eclipsed by a surface feature (eg a mountain) and so may have given a slightly low result - they were calculating the surface pressure at the altitude of this object, not necessarily at "ground level". (Kliore et al (1965). "Occultation Experiment: Results of the First Direct Measurement of Mars's Atmosphere and Ionosphere". Science, 149.)
Prior to this, the consensus in the 1950s had been about 85 mbar, based on optical measurements of the atmosphere; a more detailed study in 1964 drawing on Earth-based spectroscopic measurements had reduced this to around 25±15 mbar. (Kaplan et al (1964). "An Analysis of the Spectrum of Mars". Astrophysical Journal, 139.)
In 1969, Mariner 6 and 7 took four distinct occultation measurements at different points, with three of them agreeing on 6-7 mbar. The fourth gave 3.8 mbar, which was suggested might be due to it being measured over a large plateau. (Mariner-Mars 1969 preliminary report, p 8) By the time of Mariner 9, which took extensive orbital measurements, the data seemed to have converged on a "surface" value of 6.1 mbar, with substantial variations from 1.5-8 mbar depending on location. (Mariner-Mars 1971 scientific report, vol 4, ch 20; Hanel et al (1973). "Investigation of the Martian Environment by Infrared Spectroscopy on Mariner 9".)
So even before Viking, it seems that the current value of 6.1 mbar had been generally agreed on and is consistent with what we know today. It is significantly lower than had been estimated before the first probes arrived - but not particularly far from the very first flyby measurements.
Phoenix also did: I presume all other landers have had: I've not been able to find confirmation that Spirit and Opportunity did.
I haven't checked others not mentioned here.