Here is my list, in chronological order. I'm only including storms that I've tracked (1998-present). This list has more storms from the Atlantic than from other basins, since I watch the Atlantic more closely. Feel free to do your list however you wish!
Hurricane Lenny (1999) - eastward track across the Caribbean Sea, peak of 155mph in the second half of November

Cyclone Leon-Eline (2000) - long track from south of Indonesia to well inland Africa, remnant circulation traced all the way to Namibia

Typhoon Vamei (2001) - formation within 1.5 degrees of the equator, hit just north of Singapore

Tropical Storm Ana (2003) - Atlantic formation in April, lasted 3 days as a tropical storm

Hurricane Juan (2003) - slammed into Nova Scotia as a well-defined category 2 hurricane

Cyclone Catarina (2004) - category 2 cyclone formation in the South Atlantic, hit Brazil at peak intensity

Hurricane Charley (2004) - rapid intensification from a category 2 to 150mph in the 7 hours preceding landfall in western Florida

Hurricane Vince (2005) - hurricane formation in far northeast Atlantic near Madeira, hit Spain as a tropical depression

Hurricane Wilma (2005) - explosive intensification from category 1 to 882mb in 18 hours, tiny pinhole eye

Tropical Storm Delta (2005) - impacted the Canary Islands and Morocco shortly after becoming a strong extratropical storm

Hurricane Epsilon (2005) - lasted more than 4 days as a well-defined hurricane over waters around 72 degrees F in December

Tropical Storm Zeta (2005) - existed as a fairly organized Atlantic tropical storm for several days in January

Cyclone Gonu (2007) - tracked into the Gulf of Oman as a cyclone, hit Iran as a tropical depression

Hurricane Humberto (2007) - rapid intensification from showers to a 90mph hurricane in just 18 hours preceding landfall in Texas

Tropical Storm Alma (2008) - Pacific formation very far east, hit west coast of Nicaragua as a strong tropical storm

Hurricane Sandy (2012) - very large and deep hurricane that phased, swung west into New Jersey as a 943mb extratropical cyclone

Typhoon Haiyan (2013) - very powerful 195mph tropical cyclone, slammed into the Philippines near peak intensity

Hurricane Fred (2015) - became a hurricane east of Cape Verde, passed through the islands as a hurricane
