Succulents need grittier soil than other plants because they are adapted to dry conditions and store water in their leaves. Regular potting soil mixes stay moist for long periods of time, which can cause rot in succulents. Instead, use a gritty, well-draining soil so you can water thoroughly without leaving your succulent in standing water.
In Pots
Use a cactus / succulent soil mix from a garden center, e.g. Black Gold Cactus Mix, for varieties with thin leaves that tend to like more water
Use Bonsai Jack's Gritty Mix for varieties like cacti, Euphorbia, and Lithops (and other mesembs) that prefer extra dry conditions
Mix your own with one part potting soil, one part coarse sand, and one part pumice or perlite
In Gardens
Plant in raised beds of sandy loam
Amend heavy, clay soils with 50% coarse sand
Use a gravel top dressing to keep leaves from touching damp soil and rotting