While each species has its own unique traits and properties, all share an inherent hardiness in dry, arid conditions. However, because they evolved to exist in regions largely devoid of water for the majority of the year, they are highly suceptable to over-watering and potential rotting--either from fungus or from being waterlogged.
While plants tend to droop and wilt when they are under-watered, over-watering causes brown spots to form on leaf-tips and sometimes around the base, especially as succulents and cacti naturally conserve water as it is. Adding more to their environment than they can process, often planted in generic potting soil, is just asking for trouble.
Often, it is a matter of making sure that your soil is able to drain enough and isn't highly water-retentive, allowing excess to drain naturally. If you find there is some fungal activity, just throw out the soil your plant was in, or perhaps add it to a compost bin or pile, if you have one. If you tried re-potting something in it, that plant would likely get sick too, continuing to decompose your plants.
There are ways to try and save your plant friends in the event that you find something like this happening. I'll get to that in a later post. I think Cactus Bob, my barrel cactus friend, is going through a similar situation at the moment. I will say, if you notice something like the brown around Bob's base, as a first measure, I'd say to stop watering and move your cactus to a dry location, away from other non-succulent/cactus plants. That way, you avoid accidentially increasing the problem by watering them more with overspray. I'd also suggest either purchasing or making your own blend of cactus-specific soil.
Thanks for sticking around this long. I'd intended to talk about different species and this happened. I'll be posting more on the subject and re-planting cactus pups in the near future, so stay tuned.