A lot of people on this forum seem to say that root pruning is important for the longevity of the tree. 

Based on the picture below, should I prune these roots before putting the tree in a larger pot?  I don't know what determines when it's truly root bound.

   

When you can lift the tree out of the container without the root mass breaking apart, the tree is becoming root bound.  Depending on the tree's vigor and the size of the container, sometimes that's 2 years some can go 5 years.  If you are planning on moving up to a larger container and the tree is dormant (or not too far out), go ahead and root prune it now.  Choose a container size to hold the tree for a several years.

Root circling is not necessarily an indicator of being root bound.  It is a problem of solid, hard sided containers.

One is not suppposed to root prune until a plant is 3-4 years old. Definitely up-pot. I am planning on keeping some plants in 10 gal pots permanently, and keeping them small-sized so they are proportional. That may require root pruning every 2 years, too early to tell for me.

Whether it's root bound or not, I recommend you do the following:

Make several (maybe 4 or 5, equally spaced, doesn't have to be perfect) slices vertically along the outside edge, each going an inch or two deep.  Also, cut off that stuff that's going round and round the bottom.  I use a hand held brush hook/machete thing, but you could just use a utility knife, or anything semi-sharp really.  Make sure you don't whack your hand with it (OUCH!  luckily I had sturdy gloves on, or else would have been very bad).

If you don't do this, then in 1 or 2 years when you go to up pot to the next size, you will have huge roots circling.  Those roots along the outer edge will just get larger in diameter if they aren't put in check.  If you slice them then you don't really impact the tree's ability to take up water/nutrients, you just shorten the average length of each root.  By doing it this way you will sever almost none of the smaller feeder roots while at the same time shortening the ones that are too long. 

In a couple years you will be glad that you did this.  I am currently seeing the difference in pots where I didn't do this, and I've got these 1/4 to 1/2 inch thick roots going round and round in some pots.  Those circling roots don't do anything productive in a pot, that's for sure.  Just cause trouble.  If you don't cut them now, you'll have to cut them in a couple years when it will be much harder.

Some people say do this only when the tree is dormant, or perhaps when it's just starting to leaf out.  However, I have done it many times in the heat of summer, with no noticeable ill effects.  Not a full root prune where you cut of a bunch of feeder roots, just a slicing prune where you cut the circlers.  

Sometimes in mid summer a tree will just look wilty and crappy no matter how much I water it.  This is a sign it has become root bound.  So it's already under stress.  I can let the stress continue, or I can take it out, cut off some of those circlers, and stress it out a bit, but at least give it a chance to recover. 

I have much experience with this because I almost always wait too long to up-pot due to time constraints, so I'm always behind. 

Who says no root pruning for 3-4 years?

If you are not going to bare-root it this year, take Rob's advice.  Since roots will branch much like a limb does when it's cut, try to cut the roots off where they come out of the growing mix.  This way they will branch within the area where they can do some good.  If you are in an area with high humidity, restraint is not needed.  If not, you can cut the roots in stages about 1-2 weeks apart..  It is difficult for me to tell how much top growth you have, so exercise your best judgement.  

Bijan with all respect, who says it is right here:

http://figs4fun.com/bills_figs.html

That of course is in reference to 25 gallon SIPs.

You guys have helped me get these cuttings this far, so I will heed your advice and slice some of the roots before up-potting. 

To answer your question about how much top growth I have, see pictures below.  I started these back in September and have just started putting them outside in NJ. 

   

What I do is this....

Leave tree in it pot.
Mix up some root stimulator and water
Pour it in a large sealed pot and place the tree in the solution.  Leave it for one hour.
Next, get a new pot that at least 5 gallon or 10
Add dirt
Pull tree from liquid--using a hand rake loosen the roots and install in the new pot
Add more dirt
Add mulch and pour about 2 cups of that liquid on the new tree and place it in the shade for 3 days.

The next day go out and check on your tree.  When you do, the tree will give you a "High 5"!