Here in California, our mountains influence our weather in a particular way. We have a Mediterranean climate and big mountain ranges inland. Storms build up out on the Pacific, and they blow in toward the land. Often they hold their moisture until they get to the mountains, at which point they dump it. For this reason, the seaward sides of our mountains tend to be wetter. This would be the western side of the Sierra and the southern side of the Transverse Ranges. On the opposite side (east side of the Sierra, north side of the Transverse Ranges), we have more desert-like conditions, and the desert stretches on until you get to the Rockies. You can often see this quite spectacularly from peaks in the Transverse Ranges like the summit of Mt Baldy (San Antonio) and San Jacinto Peak: on one side is desert, on the other forests and cities.
If you look at the vegetation, you also see a slope effect. South-facing slopes get blasted with sun and tend to be brown and dry, while north-facing slopes don't get as much sun and stay greener. The slope effect is more localized than the precipitation pattern. You can often see alternating green and brown tiger stripes in the mountains.
Besides the Sierra and the Transverse Ranges, the other huge peak in California is Shasta, which is an isolated volcano cone. It does have a reputation for making its own weather, and it's said to be a bad idea to go up when there's a lenticular cloud around the summit. A physics colleague who has a background meteorology described this to me in the following way (to the best of my understanding, since he was dumbing it down for me). These lenticular clouds tend to hover around the summits of mountains. What's actually happening is that the air is not standing still. Air is flowing up and over the summit. As it rises, water droplets condense and form a visible cloud. Then as the air flows down the other side of the mountain, the droplets evaporate again and become invisible. So although the cloud stands still, the population of water droplets in it is actually constantly being depleted on one side and replaced by new ones flowing in on the other side.
You may get some similar phenomena on other big, isolated peaks in Mediterranean zones, e.g., Popocatepetl/Iztaccihuatl and Kilimanjaro. However, the rain patterns are different. Mexico's dry season is California's wet season. Kilimanjaro and Mt. Kenya tend to get rain every afternoon, like clockwork, and this pattern is superimposed on the dry and wet seasons.