Weather

Weather is a feature introduced in the Honest Hearts add-on for Fallout: New Vegas. During the gameplay, the player character can face rain during their travels around Zion Canyon. In the games preceding this the standard unchanging weather conditions where sunny or overcast, however, using weather as a feature in gameplay itself was originally considered in Van Buren, the canceled Fallout 3 by Black Isle Studios.

Fallout
Some Adytum citizens comment on the likelihood of rain soon, others note how previous rainfalls have been "glowing."

Fallout 2
In 2241, the Northern California area is suffering through a drought, the worst dry season in years, following an unusually short rainy season. Despite being relatively sustainable communities, Modoc and Arroyo were hit particularly hard. This extreme meteorological occurrence, which would go on for seven years, dominated the fate of some wasteland inhabitants.

A random encounter with a weary fisherman reveals there is apparently a regular "season of storms," not seen during the games timeframe.

Fallout: New Vegas
The sound of thunder can be heard upon fast travelling to, or just standing around, Black Mountain.

Fallout 4
The trailer for Fallout 4 revealed rain and thunder during a clip of Prydwen flying over the Paul Revere Monument. . In early game footage, fog can be seen in Sanctuary Hills

It's currently unknown if the weather has any effects on gameplay or what they could be if it does.

Van Buren
Boulder is subject to frequent bouts of acid rain, something for the player character to be aware of when traversing this area.

The Blackfoot tribe rely on the weather generated by the surrounding mountains for water, they collect rain and the winter snow.

The eastern fringes of Denver are regularly caught up in seasonal radioactive dust storms whipped up in the Midwest, making travel to certain parts of the wasteland inaccessible.

Project V13
Concept art featuring Seattle shows it, in what one would assume is winter, covered in snow suggesting regular snowfall.