We try to have a Supervisor or Lead in each department trained. We also have apprentices that have CPR/First Aid Training as a requirement.

We have everyone in the company get certified. It can't hurt, you'll never know who will be around when there is a medical emergency.

All of our security personnel are trained. Most of the EHS personnel are trained. Others are assigned training so each manufacturing area is covered, with the remainder being voluntary.

In construction, all safety personnel are typucally required to have CPR/First Aid. Depending on the size of the job, additional management staff may be required, especially on small projects without a dedicated safety member, otherwise it is usually voluntary.
In General Industry places I've worked, frequently the Maintenance department staffs the Medical and Rescue Emergency Response Teams are required to have CPR/First Aid. If equipped with Haz-mat and fire teams, they also would be required.

Mine is similar to Derek Johnson's set-up. Additionally, HR is certified. I am also getting certified in CPR this month as my previous certification was expired.