There's so many to mention but I'll just hit on some recent units.
The Aussies on the Kokodo trail in New Guinea during WWII.
3/5, 3/6/, and 1/6 Marine regiments at Belleau Wood in WWI.
Basically any Marine in the Pacific during WWII.
The Allied Army going into Normandy.
1st Mar Div in Korea(Inchon)
1st Cav Division Korea(the rest of the war)
15th Infantry Regiment in WWII(more days on the line than any other regiment in the US military during WWII)
Merrels Marauders in Burma.
The Brits and Indians at Kohima and Imphal *(spelling)
The Airborne Divisions in Market Garden
173rd Airborne in Vietnam (particularly in and around Dak To 1967)
The Finns in the Winter War...this goes without saying!
US Seal, SF, LRRP, Ranger, MACV-SOG in Vietnam
Australian SAS in Vietnam
The Soldiers and Marines of the ROK in Vietnam(my dad worked with them as a Marine in Vietnam and he said they were just awsome!)
1/9, 3/9, 26th Marines, 1/5, and 3/5 Marine Regiments in Vietnam 1967-68
FACs Vietnam
The Japanese Army in Malaya/Singapore
3rd Infantry Div and 1st Mar Div OIF 1
10th Mountain Div and 101st ABN OEF 1 (operation Anaconda)
Oh the list could go on and on, these are just a few off the top of my head.
To answer the question on US soldiers being trained in Call for fires, the answer is YES. All soldiers are introduced to Calling for fire during their initial entry training and is one of hundreds of the Basic Soldiers skills they are supposed to retain throughout their tenure in the Army. BUT, the US army has specialists in FOs and Fire Support Officers that are assigned to every Armour/Infantry company in the Army. All soldiers are expected to be able to do a basic call for fire, but since we have so many FOs, they rarely get the chance to do it. Once the soldier makes it to the rank of NCO/ Officer they much more in depth on calling for fire...like, setting up TRPs, stacking air assets, co-ordinating fires between different Mortar and Arty assets, etc.