
Pegasus Bridge, securely in British hands, is crossed by military vehicles on D-Day plus 1, June 7, 1944. The Trustees of the Imperial War Museum, London
-Brits:
Gold Beach
Special Service troops of 47 Royal Marine Commando land at Gold Beach near Le Hamel on D-Day, June 6, 1944. The Trustees of the Imperial War Museum, London
Sword Beach

Mine- and obstacle-clearing tanks of the 27th Armoured Brigade thread toward the shore at Queen sector, Sword Beach, on D-Day, June 6, 1944. The Trustees of the Imperial War Museum, London
-Canadians:
Juno Beach (en francais)

1st Hussars tanks and men of the 7th Infantry Brigade landing on a crowded beach at Courseulles-sur-Mer, June 6th,1944. Photo by Ken Bell. Department of National Defence / National Archives of Canada,
VAC site: Canada Remembers.
On board their assault landing crafts, men of the Royal Winnipeg Rifles heading towards their sector of Juno Beach, June 6th, 1944. Photo by Dennis Sullivan. Department of National Defence / National Archives of Canada,
AFAIK, the vast bulk of troops arriving on D-Day were Canadian, British, US, and French. There were 8 Australians I'm aware of attached to British forces as observers. There were scattered members of Brit forces who were from Commonwealth nations - which is not the same thing as saying, for example, that Rhodesian troops were present - though there were Rhodesians serving in Brit units that went ashore. I'm sure there was a Mexican or two in with the US forces, if we're going to get to that level of detail. And quite possibly individual soldiers of other central and south american nations.
Allied land forces that saw combat in Normandy on June 6 came from Canada, the Free French Forces, the United Kingdom, and the United States.No other allied forces of significance landed on D-Day. The Royal Air Force, with it's nationally-organized expat squadrons-in-exile, would have put some foreign contingents above or around the lodgement area. And there were individual naval vessels-in-exile, too.
In the weeks following the invasion, Polish forces landed, as well as contingents from Belgium, Czechoslovakia, Greece, and the Netherlands. Most of those countries also provided air and naval support for the campaign, along with the Royal Australian Air Force, the Royal New Zealand Air Force, and the Royal Norwegian Navy.
But when we talk dropping or wading in, on D-Day, we're talking Britain, Canada, the United States, and France.