All times UTC. Adjust for your own time zone. [Pacific: subtract 8. Mountain: subtract 7. Central: subtract 6. Eastern: subtract 5. Other parts of the world: look it up!] Some Southern Hemisphere countries seem out of place according to a time zone map because they're currently observing DST. Russia is divided up into several time zones, each one indicated in this list by the name of a prominent city within it (except "central Siberia"; the map I was looking at had no cities listed for it).
Mon Dec 31
10:00 am - Line Islands (Wow, this is 4 am for me! Less than 3 hrs to go!)
10:15 am - Chatham Islands
11:00 am - Tonga, Phoenix Islands, New Zealand
noon ----- Petropavlovsk, Marshall Islands, Tuvalu, Fiji
12:30 pm - Norfolk Island
01:00 pm - Magadan, Kuril Islands, Solomon Islands, Vanuatu, New Caledonia, Lord Howe Island, New South Wales, Victoria, Tasmania
01:30 pm - South Australia
02:00 pm - New Siberian Islands, Vladivostok, N. Mariana Islands, Micronesia, Papua New Guinea, Queensland
02:30 pm - Northern Territory
03:00 pm - Yakutsk, Korea, Japan, Palau, eastern Indonesia, Western Australia
04:00 pm - Lake Baikal, Mongolia, China, Hong Kong, Macau, the Philippines, Malaysia, Singapore, central Indonesia
05:00 pm - Severnaya Zemlya, central Siberia, Thailand, Laos, Cambodia, Vietnam, western Indonesia
05:30 pm - Burma, Cocos Islands
06:00 pm - Omsk, Novosibirsk, most of Kazakhstan, Kyrgyzstan, Bhutan, Bangladesh, Sri Lanka, British Indian Ocean Territory
06:15 pm - Nepal
06:30 pm - India
07:00 pm - Perm', the western bit of Kazakhstan, Uzbekistan, Turkmenistan, Tajikistan, Pakistan, the Maldives, Île Amsterdam, Île Saint-Paul, Îles Crozet, Îles Kerguelen, Heard Island & McDonald Islands
07:30 pm - Afghanistan
08:00 pm - Samara, Georgia, Armenia, Azerbaijan, Oman, the Seychelles, Mauritius, Reunion
08:30 pm - Iran
09:00 pm - Franz Josef Land, Novaya Zemlya, Moscow, Iraq, Kuwait, Saudi Arabia, Bahrain, Qatar, Yemen, Sudan, Eritrea, Ethiopia, Somalia, Uganda, Kenya, Tanzania, Mayotte, Madagascar
10:00 pm - Finland, Estonia, Latvia, Lithuania, Belarus, Ukraine, Moldova, Romania, Bulgaria, Greece, Turkey, Cyprus, Lebanon, Syria, Israel, Jordan, Egypt, Libya, eastern Dem. Rep. of the Congo, Rwanda, Burundi, Zambia, Malawi, Mozambique, Zimbabwe, Botswana, Namibia, South Africa, Swaziland, Lesotho
11:00 pm - Svalbard, Jan Mayen, Norway, Sweden, Denmark, Poland, the Czech Republic, Slovakia, Hungary, Slovenia, Croatia, Bosnia and Herzegovina, Serbia, Montenegro, F.Y.R.O.M., Albania, Italy, Switzerland, Liechtenstein, Austria, Germany, the Netherlands, Belgium, Luxembourg, France, Spain, Tunisia, Algeria, Niger, Chad, Benin, Nigeria, Cameroon, Central African Republic, Equatorial Guinea, Gabon, Rep. of the Congo, western Dem. Rep. of the Congo, Angola
Tue Jan 01
midnight - Iceland, the U.K., Portugal, the Madeira Islands, the Canary Islands, Morocco, Western Sahara, Mauritania, Senegal, the Gambia, Mali, Guinea-Bissau, Guinea, Sierra Leone, Liberia, Côte d'Ivoire, Burkina Faso, Ghana, Togo, São Tomé and Príncipe, Ascension, St. Helena, Bouvet Island
01:00 am - Itseqqortoomiit, the Azores, Cape Verde
02:00 am - Fernando de Noronha, southeastern Brazil, Uruguay, Argentina, S. Georgia and the S. Sandwich Islands
03:00 am - Greenland, St. Pierre & Miquelon, Suriname, French Guiana, northeastern Brazil, southwestern Brazil, Paraguay, Chile
03:30 am - Island of Newfoundland
04:00 am - Qaanaaq, Labrador, New Brunswick, P.E.I., Nova Scotia, Bermuda, Dominican Republic, the Lesser Antilles, Trinidad & Tobago, Venezuela, Guyana, northwestern Brazil, Bolivia, the Falkland Islands
05:00 am - Ellesmere Island, Baffin Island, Québec, central and eastern Ontario, Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsylvania, Michigan, Indiana, Ohio, West Virginia, Maryland, Delaware, Virginia, eastern Kentucky, North Carolina, eastern Tennessee, South Carolina, Georgia, Florida, the Bahamas, Cuba, Haiti, Jamaica, the Cayman Islands, Panama, Colombia, Ecuador, Peru, the western tip of Brazil, Easter Island
06:00 am - Nunavut, Manitoba, western Ontario, Wisconsin, Illinois, northwestern and southwestern bits of Indiana, western Kentucky, western Tennessee, Alabama, the western tip of Florida, Mississippi, Minnesota, Iowa, Missouri, Arkansas, Louisiana, most of N. Dakota, eastern S. Dakota, eastern Nebraska, most of Kansas, Oklahoma, most of Texas, most of Mexico, Guatemala, Belize, El Salvador, Honduras, Nicaragua, Costa Rica, Galapagos Islands
07:00 am - Northwest Territories, Alberta, Montana, southwestern N. Dakota, western S. Dakota, western Nebraska, Wyoming, southern Idaho, most of Malheur County in Oregon, Colorado, four counties on the western border of Kansas, Utah, New Mexico, the two westernmost counties of Texas, Arizona, Sonora, Baja California Sur, Sinaloa, Nayarit
08:00 am - Yukon, British Columbia, Washington, northern Idaho, most of Oregon, Nevada, California, Baja California, Clipperton Island, the Pitcairn Islands
09:00 am - Alaska
09:30 am - Îles Marquises
10:00 am - the Aleutian Islands, Hawaii, French Polynesia, the Cook Islands, Tokelau
11:00 am - Midway Atoll, Kingman Reef, Palmyra Atoll, Jarvis Island, Samoa, American Samoa, Niue
noon ----- Howard Island, Baker Island