This is based on preliminary information from diverse sources. Caveat lector.

January 2015 was warmer than average1 across South America, the northwest of North America and large areas of Eurasia, including China where it was the warmest January on record. Colder than average conditions were observed across the northern half of Africa, Mexico and the eastern side of the US and Canada. The Iberian Peninsula, India, parts of Australia and an area on the north coast of Russia were colder than average. map 

Despite general warmth over Russia, there were some areas of cold. At the station Hoseda-Hard in the Nenets Autonomous District a temperature of -51.5°C was recorded, only half a degree above the record low.

Sea-surface temperatures continue to be warmer than average in the north-east and tropical Pacific (looking more +ve PDO than they did this time last year) . Areas of above average SST area also seen in the North and South Atlantic, but we have colder than average SSTs in parts of the tropical Atlantic and in an area just south of Greenland. The Indian Ocean is largely warmer than average. Large areas of the South Pacific and Southern Ocean are cooler than or close to average with two obvious exceptions – an area in the south east and an area between Australia and New Zealand.

Precipitation totals were greater than average in the southern US and northern parts of Mexico, parts of western South America, Europe, central Asia, southeast Asia (around southern China, Myanmar, Laos), northern and eastern Australia, Mozambique and Madagascar. Drier than average conditions were observed for large areas of Africa – southern Cameroon, most of Gabon and Congo, northern DRC, most of Uganda, bordering area of Angola, Namibia, Botswana Zimbabwe and Zambia, according to ACMAD – Brazil, Chile and the southern tip of Argentina, the Middle East, the west coast of the US (including Alaska), New Zealand (SAM was largely +ve from mid-December to mid-February), and southwest Australia. map

Chile was drier than average throughout the country with the south of the country seeing the most extreme deficits. In places it was the driest January in at least 50 years. The Stations of Temuco and Valdivia recorded no rainfall during the month, Osorno and Puerto Montt recorded 1.8 mm and 9.6 mm respectively.

The heavy rain in south east Africa led to flooding in Malawi. As of 27 January, the floods had affected an estimated 638 000 people and killed at least 79 people, while 153 were still missing. Flooding also affected Mozambique (affected 160,000 people and killed 158) and Zimbabwe (6000 affected).

Frequent high intensity showers fell in Malaysia, Indonesia and the Philippines. The rain fell on areas where rainwater that fell in December water had still not gone from the fields and caused flooding.

In Australia, cold wet conditions were observed from Tasmania up through to the northern territory. A number of locations recorded their wettest January on record or wettest January day on record. Away from this band of misery, some locations were warmer and even drier than average.

In Fiji, two stations recorded record high daily max temperatures for January and another recorded a record high daily minimum for the month. Lakeba recorded a record monthly mean of 31.7C breaking the record set in January 2014 of 31.4C.

Snowfalls hit Syria, Lebanon and northwest Saudi Arabia at the beginning of the month on.

Tropical Storms
NW Pacific – Typhoon Mekkhala 13-18 January (disturbed the Pope)
SW Pacific – Tropical Storm Niko 20-24 January
Cyclone Ola 30 January-3 February
SW Indian – Cyclone Bansi 11-18 January
Tropical Storm Chedza 16-18 January
Tropical Storm Diamondra 26-29 January
Cyclone Eunice 27 January-2 February

Less interesting country summaries (some of these might break when February rolls around)…
Germany a station reported a temperature above 20C the first time this has been recorded in January.
Spain (a kind of interesting precip pattern – very wet along the north coast, dry elsewhere).
Austria (At Obervellach a temperatures of 21,7C was recorded on 10 January, a new record for January for the country)
Ireland (second sunniest January at Dublin airport since 1941)

1: 1961-1990 averages unless I say otherwise and this is based on the GISTEMP data set.