Everything from more tornadoes to stronger hurricanes to a colder winter.
From NOAA's CPC via the National Weather Service's Gand Forks office:
The NOAA's Climate Prediction Center (CPC) has issued a La Niña Watch for the upcoming late summer and fall season. La Niña refers to the periodic cooling of ocean surface temperatures in the central and east-central equatorial Pacific that occurs every 3 to 5 years or so. La Niña represents the cool phase of the El Niño/Southern Oscillation (ENSO) cycle, and is sometimes referred to as a Pacific cold episode. La Niña originally referred to an annual cooling of ocean waters off the west coast of Peru and Ecuador. Similarly, El Niño refers to the large-scale ocean-atmosphere climate phenomenon linked to a periodic warming in sea-surface temperatures across the central and east-central equatorial Pacific (between approximately the date line and 120oW). El Niño represents the warm phase of the El Niño/Southern Oscillation (ENSO) cycle, and is sometimes referred to as a Pacific warm episode. El Niño originally referred to an annual warming of sea-surface temperatures along the west coast of tropical South America.
Both El Niño or La Niña produce changes in Pacific Ocean temperatures, which affect the patterns of tropical rainfall from Indonesia to the west coast of South America. These changes in tropical rainfall affect weather patterns throughout the world. (Click to read more on how El Niño and La Niña change tropical rainfall patterns.
Typically, La Niña produces a cooler and wetter winter season across the northern plains. However, every La Niña and every El Niño interacts with other large scale atmospheric patterns including the Pacific Decadal Oscillation (PDO), the Arctic Oscillation (AO), North Atlantic Oscillation (NAO) as well as several others. These other climate signals can diminish or exaggerate the impact a La Niña or El Niño has on our weather. For example, the 2009/2010 El Niño reached moderate intensity, yet the overall winter season in portions of the northern plains was cooler and slightly wetter than average....