When I was in from 1983-1993, tattoos were a rare thing to see.
I think the first time I remember really seeing a lot of guys get them was in 1990, in the lead-up to the Gulf War. The expectations at the time (I was Infantry remember) was that this was going to be a bloody conflict, with high casualties. So I knew a lot of guys that got "Meat Tags", which at that time was just basically a copy of your dog tag information under your left arm.
Even I almost got one, until I was injured in a motorcycle accident and had to sit out that conflict on Fort Couch.
But today, even that meat tag is a lot more elaborate.
But I do not have a real issue against these, because nobody sees them at all when you are in uniform, and they do fulfill a real purpose.
And I think a lot of Marines still avoid them (especially Infantry) because having one as mak2 stated, they really kill your chances to get those privileged "B Billets" like Embassy Duty, Sea Duty, and Barracks Duty (the later I was able to do twice during my career). With tats, you are stuck your entire career in "The Fleet", doing grunt games and getting eaten up by chiggers and ticks.
Without them, you get to be stationed in places like Guam, Spain, England, and a great many other privileged locations. And while there are some slots for non-grunts at these duty stations, 90% of the slots are for 0300 MOS only. And with the advent of FAST Company, that is probably the second most elite unit in the Marines (next to Force Recon).