I think at a minimum everyone should have a kit for home
Got this one for the garage at Costco:
From First Aid Exchange - easy to refill as each section is marked. Mounted to wall in garage next to workbench
We also keep one in the Kitchen and Bathrooms:
I am a docent with the Laguna Consevancy and need to carry light but good kits for hikes and biking. One of the biggest things we carry is aspirin (heart attacks) and Benadryl (allergic reactions to stings etc) and tick removers. REI has some of the best pre-packed kits and have all sorts of options there:
http://www.rei.com/camping/TOC/First+Aid?cm_re=toc*toc*first_aid&vcat=REI_SSHP_CAMPING_TOC
The car depends on the trip/event... I have back-packs with everything from first aid to survival (three day). These can be expensive (we get them through our CERT program at work) but also can be made and there are many sources that can provide that info (FJ Forums has some good ones by our own So Cal members) - check out American Red Cross for starters...
http://www.redcross.org/services/hss/lifeline/fakit.html
Best advice I got (cause I know others will list their kits and have much more info) is get training in First Aid, CPR and AED (Automated External Defibrillator) as these are much more popular today.