Haven't done much in Europe, but:
New Zealand - Tongariro Crossing/Circuit, Mount Ruapehu, Mt Ngauruhoe (North Island), Routeburn, Queenstown Hill hike (South Island). Mt Taranaki also, but I've been turned back by storms both times :-(
Australia - Cradle Mountain Tasmania and other hikes in the NP, anything around Freycinet NP, Tas. Coastal Walk in Royal National Park, Cliff track in Tasman National Park (forget the trail name); Sydney - coast walk from Bondi to Coogee (paved, but great ocean shoreline views), Blue Mountains.
Chile - Torres Del Paine "W" or "Full" circuit and any of the side trips nearby.
Argentina - Fitz Roy Circuit and any side trips nearby
Japan - Daisetsuzan NP alpine trek, beautiful scenery and wildlife; Shirotoku is also wonderful, but plenty of Brown bears there (Higuma) to watch out for, lots of deer also.
Canada - Waterton lakes NP (sister of Glacier in the U.S.)