running lots- how much is lots?

Yes, running more often will make you faster.  How much faster depends on a lot of things.

I don't know anything about your fitness, but 2-3 20 minute jogs being part of running 5-6 day a week sounds perfect.  The key to adjusting to running more often is to make sure you run easy.

So... say one would be running 12 miles per week.  I read those threads to say,   Better to do, say, 2 x 1.5 miles, 3x2 miles, and 1x3 miles, than 5, 4, 3.  But you are saying, that won't really help anything?

But you seem to say- you will get faster if you do, say, 3x3 and 3x2 (so get in 15 miles overall)?

And I know- 15 miles is a really small amount for anyone who's serious about running.  I'm not that serious about running (obviously) but if 15 miles 6 days a week would make me much faster than 12 miles 3 days, well, sure I'll do that.  But does anyone think that will really help?

I think that I was one of the ones who sang the virtues of running even as little as 10 minutes a day as a part of a run-often plan. 

To clarify (and to echo part of what Shane already said): it's not that doing frequent short runs will suddenly make you faster. Rather, it's a great way to start building towards running rather more miles, while minimizing injury risk. If you run steady every day, then you should quickly find that it's not hard to increase the length of the runs. That's when you start to see the real benefits of the mileage, and that's when the fitness gains really start to show. That volume should, in principle, also better prepare your body to handle occasional higher intensity runs, again with reduced injury risk. 

Quite apart from that, I find that I really enjoy my daily fix of steady running. I feel great afterwards.

Your first assumption was correct. Running lots means lots of miles. One of the best ways to run lots of miles is to run lots of days. Because many people don't run lots of the days, advise has been given to add in short runs on days these people don't normally run. Once people get used to running frequently it's usually better to even out the daily running unless they are training specifically for some race. Your example of doing 3x2 & 3x3 is good. Now by simply adding .5 miles to each of those runs once every other week or so, you can grow the overall volume fairly quickly. For many people that only adds another 5 minutes or so to their runs. So without overly stressing the body it's possible to grow the volume up to 25-30 miles/week within a few months. That's when you're likely to start seeing improvements to your speed. Frequency, consistency over a longer time frame and bingo - faster running. Where many people fail is they don't keep at it long enough to see the improvements. Keep it up for at least 6 months. The more you can gradually add to the weekly volume the better - up to a certain point.

Have fun!

Yes ... as has been clarified ... more running means more mileage. To run better you have to do more of it from an overall mileage sense. Add those miles slowly, tough. The 10% rule is a good one, but I think you can add more than that to a smaller load.

The key is to run more miles slowly. You should have a couple of key run workouts per week for which you are well rested. This means running the rest of your miles at either a recovery pace or a slow GA (general aerobic) level. It is crucial to realize that the fastest runners are not running every run at their fastest pace. I'm a sub 1:30 half marathoner and a 3:10 marathoner and my recovery miles are all run close to a 9min/mile pace. Then, when I hit the track or a LT run, I've got the energy to really make it count.

Let me say it one more time ... more miles run more slowly than you'd think. 

Running 5-6 days a week is a great idea. Setting a training plan is important. It's easier to have a routine where have more days on than off. You'll come to expect running and it will actually be more stressful if you miss a day. By keeping the mileage and pace to a reasonable level you will also minimize the possibility of injury, as has been said.

Keep a log, it is great motivation as you keep putting "another one in the books." Looking back and see the miles run and the weight lost is just huge.

Ok so I get that overall running volume is necessary to increase speed and endurance.  Makes sense.  But I also hear recommendations of putting 150 mile weeks in on the bike, that's what? 8 hours of riding a week?  And don't forget swimming?  10,000-15,000 yards a week?  what are we up to now?  Seems like even on here, a triathlon specific forum, the same volume recommendations that are given for these sports by them selves are given for each of the three. 

When I started biking and swimming regularly my running volume had to take a hit.  Is this not the case with everyone or do I just not have as much free time as others do?

And there in lies the problem.  Sometimes the interest and the time don't seem to be in agreement... Someone needs to find a way to manufacture more hours.

Yup. And when you throw family into the mix it just adds to the dynamic. You can still do it, but it might mean swimming at 6am before work and biking on the trainer/running on a treadmill when everyone else goes to bed.