According to a report by the National Research Council, "climate change will affect every type of transportation through rising sea levels, increased rainfall and surges from more intense storms." At the same time that concentrations of carbon dioxide in the atmosphere rise to dangerous levels, "people continue to move into coastal areas, creating the need for more roads and services in the most vulnerable regions." The threats to transportation infrastructure range from the obvious (sea level rise and storms will damage bridges and roads and disrupt air and ground traffic) to the, well, slightly less obvious (heat waves will cause "thermal expansion of bridge joints and rail track deformities.")
The key finding of the report is that transportation planners will have to start taking climate change into account when they design transportation systems. Of course, that means shelling out more money up-front which, though it usually reaps long-term benefits, doesn't sit well with election-cycle thinking. It also means considering the carbon emissions associated with different systems (e.g., highway vs. bus rapid transit). The existing transportation infrastructure needs upgrading for many reasons, not least of which the fact that it "was built for local conditions based on historical weather data" which may no longer be accurate given a changing climate.
See Also: Solar Roadways: Energy-Generating Roads Made Out of Glass and Solar Cells, ::Sustainable and Sound Infrastructure Now, ::Can BRT Encourage Bike Use? and ::US Secretary of Transportation Says Bikes "are not transportation"