Do GA pilots routinely request "flight following" from ATC, and why?
I typically like to get VFR flight following if I haven’t filed a flight plan for longer distance flights. The biggest advantage here is that somebody knows where I am if something should happen. 

I don’t typically find the chatter too bad, but you do have to be on the ball, especially when handed off from a local airport to an Air Route Traffic Control Center (commonly referred to as just “Center”) frequency. Often on flights out of my airport (KGRB) I will get handed off to Minneapolis Center, which is relatively busy frequency. 

Another nice thing is that it gives you some practice talking in busy airspace. You really have to follow the rules and jump in when able. Sometimes they won’t hear you because you are transmitting over other aircraft that you can’t hear, so the frequency will appear open. It’ll sound like they are talking to themselves. 

So here is how I see it:

Pros


You are talking to somebody and working with other traffic in the airspace
You are on a frequency you can broadcast an emergency to. Yes we all know about 121.5, but you are not guaranteed to get somebody on the other end.
ATC knows where you are, and if you fall off the radar and don’t respond, they will initiate a search. If you just file a VFR flight plan they won’t even start until 30 minutes after your planned arrival, and then they start calling airports and contact numbers, then start a search. They may not know where you fell off your flight plan so the search area is much bigger.
They can help route you around active MOAs, TFRs, and other airspace/weather issues that don’t show up well on paper maps.
Traffic advisories (as others pointed out)
Can provide a vector to where you want if you get lost.
Don’t need to open a flight plan if you can get following all the way.
Good radio practice


Cons


Flight following is “workload permitting.” They may call up and say Radar services terminated; squawk VFR at any time, turning your flight back into normal VFR. If you didn’t file a flight plan, now you should call up FSS and open one en route, which is more difficult.
Requires you to be on-the-ball with your radio transmissions on busier frequencies. If you frequently fly from uncontrolled airspace, this can be intimidating. 
You may get vectored around a bit, but I usually don’t have that problem. I’ve typically contacted the destination airport by 20 miles out and either got clearance or vectors anyway.