There are lots of scriptures about patience... (As you read them note the relationship between faith, hope and patience.)

Luke 21:19  In your patience possess ye your souls.
Rom 5:3-4  And not only so, but we glory in tribulations also: knowing that tribulation worketh patience;  And patience, experience; and experience, hope:
Rom 8:25  But if we hope for that we see not, then do we with patience wait for it.
Rom 15:4  For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope.
Col 1:11  Strengthened with all might, according to his (Jesus') glorious power, unto all patience and longsuffering with joyfulness;
1 Th 1:3  Remembering without ceasing your work of faith, and labour of love, and patience of hope in our Lord Jesus
2 Th 1:4  So that we ourselves glory in you in the churches of God for your patience and faith in all your persecutions and tribulations that ye endure:
Heb 6:12  That ye be not slothful, but followers of them who through faith and patience inherit the promises.
Heb 10:36  For ye have need of patience, that, after ye have done the will of God, ye might receive the promise.
(And many more)

Below I have taken James 1:2-4 and broken the passage down in the Greek and then reassembled it back into English in order to expand it and make its meaning even more clear to you than ever before.  Particularly, its revelation of patience's relationship to faith.
 

James 1:2-4 Expanded:

Note that in my amplification, that key words and phrases are in bold.  I did this to draw your attention to some of the details.  Lets step through the whole thing.

First we see to whom he (James) was writing - the Church.  If you are a born-again baptized believer, then this letter is to you.

He says "account it" in the sense of an accountant accounting an expenditure to a specific category or column in a ledger.  The category you are instructed to "account it" to is the 'Joy / Cheerfulness' column as a credit to that account.  He says to do this every time you accidentally fall into temptation or situations that try and test your faith.  The implication is that as long as there is a devil loose in the world, temptations and trials will be dug like pits in our path to capture us as we progress along our way believing and trusting God.

That's really what real Bible faith is.  Faith is believing what God's written Word says - so much - that you 'step out' upon what it says, and act upon it.

James says to account it as a credit in that column - in advance - knowing something.  Well it implies that you know in advance that you are going to have a joyous victory.  And, know that when temptations and trials come to question, test and try your faith - that it does something to your patience. 

Now the patience James is talking about here is - in the sense of "standing - completely in control - while under pressure,"  similar to the passage in Eph 6:13-14 which says, "Wherefore take unto you the whole armor of God, that ye may be able to withstand in the evil day, and having done all, to stand - stand ..."  He is talking about patience as you are standing in faith.

James says that when pressure is placed on your faith, it gives your patience, which supports that faith - a workout.  And, in addition to that, the pressure helps you by showing how and where to distribute or redistribute the patience you have.  And, that you can count on patience, because when you specifically target patience to support an area of your faith, not only will every little bit of patience not fail - but all of your patience will work together as a superstructure which, will support your faith and will never fail.

Praise God!  I don't know how that effects you, but that excites me!

Here is an illustration of what I'm saying...
 
Here is a railroad trestle.

Lets consider this our bridge of faith. (Note that a series of "F's" make a railing for the bridge.)
If there were no poles to hold the trestle up it would sag or fall under its own weight.

Lets say that each set of poles in our picture support a particular area of your faith - (Let's say from left to right: Salvation, deliverance, protection, healing, financial provision).
Right now there is evenly distributed support for all of these areas, but what would happen if one area had no support? ( i.e. If the support was not evenly distributed...) 

Currently there is no pressure to test it as to whether it will stand on not.

But, now here comes temptation, trials and testing - putting pressure on each area of your faith.

The poles are your patience.  (Note that I have used the letter "P" to denote each pole.)  Patience is what supports your faith.

As temptation, trials and testing apply pressure to each area, it is your patience in that area that under girds and supports your faith.
If patience is lacking in a particular area, your faith will begin to sag.  (Let's say in the area of finances or healing.)  
But rather than panic, rejoice!  Because, by seeing your sagging faith in that area, you know how and just where to redistribute your patience!  And once in place, your patience ties itself together as a unit even stronger than the sum of its parts!  
Guaranteed not to fail!