I can speak from my and my son's experiences.
I was a USAF cop in the 1960's and was never issued a knife. I think our personnel in SE Asia were provided with M-7 bayonets. I provided my own. I carried an I*XL scout knife (bought from Randall) in my parka or flight jacket and a Swiss Army Spartan in my right trousers pocket. Those were all I had on duty. We couldn't carry sheath knives stateside, but I bought a Gil Hibben (then called Ben-Hibben) Jungle Fighting Knife in case I was sent to Vietnam. I had a Randall Model 3 with the usual leather handle and a Buck Pathfinder Model 105 and a Solingen - made (Bavarian pattern) knife by Anton Wingen (Othello marked) for hunting and fishing while off duty. I still have the Othello knife and the scout knife by I*XL. The Buck was lost or sold as was the Randall, but replaced ASAP. The Hibben was also sold to pay college expenses. Thankfully, I now have ample knives.
My son did three tours in Iraq in the Army as both infantry and as an artillery fire control specialist, and as a division staffer. In the latter capacity, he often led raids looking for senior Iraqi officials and also escorted and advised dignitaries and media personnel.
I offered him a Fallkniven S-1 with the black Ceracoated blade. I thought it would prove effective as a multi use knife with combat capability, if needed, and small enough to conceal, if required. He took it as a gift, but decided that it was too nice and too expensive to risk in a combat zone, where an aggressive commander or customs bureaucrats might have it confiscated. He took instead a Camillus-made "K-Bar" USMC knife, a Leatherman tool, and carried a cheap Chinese one-handed folder on the last tour, where he was a security contractor. Someone he knew passed out some, and he cherishes it for nostalgic reasons. His EDC now (out of the Army) is a Benchmade with a four-inch (?) tanto blade, with which he defended himself from an attack by a large coydog. The dog ran off after being stabbed as it went for his throat, but was probably mortally wounded.
He was often in very heavy fighting and had to resort to a pistol at times, but was glad that he never had the enemy get so close as to require use of a knife. But the Ka-Bar was there, if needed, and a comfort.
I think many commanders now frown on the carrying of large sheath knives, outside of the elite special ops people. I believe some of this is due to pressure from liberal social values and a desire by commanders to avoid any injuries that would damage their safety records. There are also ethnic/demographics reasons that I'm afraid to address on most message boards. And many commanders come from liberal areas where knife laws are strict or have gone to public schools where they "learned" that even basic pocketknives are evil.
I know of an El Salvadoran soldier in Iraq whose unit was all killed by insurgents and he was out of ammo. He drew a lockblade folder and charged the advancing enemy, killing and wounding several and routing them. For this , he received the El Salvadoran equivalent to the Medal of Honor. Some of you may have seen a photo of him on the Net, showing him displaying that knife. I couldn't determine the brand. It looked to have about a four-inch blade, a spear or drop point shape. There was (if memory serves) a large brass or nickle silver forward bolster. This is the only case that I have personally encountered of a knife being used in battle recently, but I may well have missed some, and some may never be reported.
For over 30 years, I wrote professionally about knives, for cutlery magazines.
One day, I was in the late G.W. Stone's shop interviewing the custom maker for a profile story. He showed me a letter from a Special Forces guy in Vietnam who said that he took off the head of a VC soldier with one hard whack of his Stone Model A, with either a seven or eight-inch blade; I forget which. I'm sure there are unpublicized combat uses of the knife in most wars.
But by far the most common use of a military knife is in normal utility roles.
For the record, if I was able to carry whatever I wanted in a combat zone today, it'd probably be a Fallkniven A-1 and a Victorinox pocketknife, either a Spartan, the older Swiss Soldier knife with silver Alox scales, or a Bundswehr knife of the sort once made for Germany by Vic. and a number of other contractors. Someone posted a link to see one of those on Amazon.com. See the above posts. Actually, I'd want that Bundeswehr folder in a jacket pocket and the Spartan or former Vic. Soldier on my person. If I couldn't afford a Fallkniven or a Randall Model 5 or 14, I'd want a Buck Model 119. The brightly polished pommel and guard might prove too reflective, but tape can cover those parts in a combat zone.
In a conversation with a Gerber PR man, he mentioned that they sell a lot of their Applegate-Fairbairn folders to troops in Afghanistan. Some carry them in pouches on their vests. I like them a lot, too, but mine came so dull that I had a custom knifemaker reprofile the edge bevels and hone them.