At my Volunteer Fire Department in WV, a second alarm on a structure fire will typically bring a couple of engines, a ladder, and possibly a tanker (if there are not hydrants available). A third alarm for us means that all hell has broken loose and departments from as far as an hour away are enroute, and the county Emergency Services Coordinator is contacted. In my 10 years at this department (I did a 7 year stretch at another), we've called a third alarm twice: a large warehouse fire with multiple exposures, and a Dollar General Store fire with exposures (including an attached Post Office, which we saved.) The warehouse fire brought over about 100 firefighters from 11 departments, and the Dollar Store fire had about 80 firefighters from 7 departments. Lucky me... I was Senior Captain and sector command for both incidents.
Until just recently, the municipal water supply was substandard to say the least, so most 2nd and 3rd alarm callouts included tankers and supertankers (~4,000 gallons.) Like nozzlenut83 said, larger departments typically have a more standardized callout for each alarm, where smaller departments may advise dispatch what their needs are when they call for additional alarms.