Air Traffic Control
Air Traffic Control (ATC) are often a major source of weather information for pilots. Modern ATC radars often overlay weather radar over the screen so ATC can assist pilots in avoiding weather. In terminal areas ATC may be equipped with additional systems such as terminal doppler weather radar (TDWR) or low-level windshear alert system (LLWAS). If able, ATC will impart any weather information they have to pilots to assist them in choosing the safest course. That's an ideal scenario of course and sometimes ATC isn't helpful.
En Route Flight Advisory Service (EFAS or Flight Watch)
A service specifically designed to provide timely en route
weather information upon pilot request is known as the en
route flight advisory service (EFAS), or Flight Watch. EFAS
provides a pilot with weather advisories tailored to the type
of flight, route, and cruising altitude. EFAS can be one of
the best sources for current weather information along the
route of flight.
A pilot can usually contact an EFAS specialist from 6 a.m. to 10
p.m. anywhere in the conterminous United States and Puerto
Rico. The common EFAS frequency, 122.0 MHz, is established
for pilots of aircraft flying between 5,000 feet above ground
level (AGL) and 17,500 feet mean sea level (MSL).
Hazardous Inflight Weather Advisory (HIWAS)
Hazardous Inflight Weather Advisory (HIWAS) is a national
program for broadcasting hazardous weather information
continuously over selected navigation aids (NAVAIDs). The
broadcasts include advisories such as AIRMETS, SIGMETS,
convective SIGMETS, and urgent PIREPs. These broadcasts
are only a summary of the information, and pilots should
contact a FSS or EFAS for detailed information. NAVAIDs
that have HIWAS capability are depicted on sectional charts
with an “H” in the upper right corner of the identification
box.
XM
Many modern avionics systems receive NEXRAD over XM as well as a myriad of other weather sources. Avionics suites such as the Garmin G1000 give pilots access to NEXRAD overlay over a map as well as a visual display of METARs, TAFs, FDs, PIREPs and many other weather information sources. There were a lot of acronyms there, but they can all be referenced in the two references provided at the bottom of this answer.
On-board Radar
Many aircraft are equipped with radar on-board. This provides a major step up from NEXRAD for making specific choices. Some pilots may disagree, but I view NEXRAD as a way to make "overview" choices about weather. NEXRAD is often too far delayed or affected by errors to make fine-grain choices. On-board radar can be directed at the airplane's altitude and provides an immediate picture of what's happening.
I also read the article from ForeFlight about the Airbus that got into hail. It's true that many general aviation aircraft have more in the cockpit that airliners. I'm not sure if airline pilots are allowed to use additional sources from things like ADS-B receivers they bring with them, but my guess is that while it's probably not forbidden, it's a risk to the pilot. If a situation arose where a pilot made a decision based on information from an unofficial source and it lead to a bad result it could be detrimental for the pilot and the airline. Most pilots probably stick to their official sources.
For pilots flying under the FAA, two good sources for the answer are the Pilot's Handbook of Aeronautical Knowledge (PHAK) Chapter 13 and AC 00-45G. Chapter 13 of the PHAK is dedicated to aviation weather services, many of chich are available in flight. AC 00-45G is dedicated to the same, it just tends to be updated a little more often and goes into greater detail.
Generally speaking though I have found that FAA materials haven't done the best job in keeping up with the fast pace of technology and its modernizing effects on avionics. Then again, the modern technologies are usually repackaging existing weather services and providing them in a better interface.
