CRM is not just crew anymore - it's now typically referred to as "Cockpit Resource Management" (or in some cases, when no crew is present, as "Single-Pilot Resource Management") and it's something the FAA emphasizes on all checkrides.
CRM includes all resources available to any pilot. In a typical light GA aircraft this means checklists, instruments, gauges, radios, and nav. However, ATC is a resource, especially during abnormal or emergency situations. So is FSS, Unicom, or even other aircraft nearby (think relaying an IFR cancellation etc).
In a large aircraft, CRM obviously includes your flight and cabin crew, plus other airline or corporate perks like dispatch.
The safety improvements come from knowing when to offload work or call on systems or people for assistance. Even a non-pilot passenger can be a huge help in spotting other aircraft, tuning radios, rummaging around for your spare pen... that's all CRM and lets the pilot focus on flying.
From the Private Pilot PTS (FAA-S-8081-14B):
Special Emphasis Areas
Examiners shall place special emphasis upon areas of aircraft operations considered critical to flight safety. Among these are:
15. Single-Pilot Resource Management (SRM), and
16. Other areas deemed appropriate to any phase of the