If you play a variety of music in a variety of keys the standard tuning is your best bet because it is so flexible and because you can change keys without changing your patterns (unless you run off one end of the neck or the other!). If you play certain kinds of music that evidently are written in a few or only one key then changing your open strings to a pattern that is optimum for that music/key may be helpful. At least this is what I am told, I evidently don't listen to or play that music. 
This is not without historical precedent, before even tempered tunings became the norm, keyboard instruments would be tuned to suit a narrow range of keys and would sound wildly out of tune in other keys. Guitars have their frets put in the even tempered locations so no problem with them but the old viola de gamba family of stringed instruments used tied on frets that could be shifted to optimize their locations for a given key. Even today violin family string players will finger notes differently to suit the key they are playing in and they will finger differently when playing a solo than they do when playing in the ensemble.
Even if you stick with a "standard" tuning you have valid choices to make. Many will tune their four strings BEAD to pick up the notes between B and E on the bottom string. That is still a standard tuning because it is in fourths. Then there are a few of us who tune a four string CGDA. This is also a standard tuning but it is the violin family standard tuning in fifths. The advantage here is that you get the range of a five string tuned in fourths without the bother of that fifth string! As has been mentioned it will change your familiar patterns and it usually makes them easiest to play on two strings rather than three which can result in a lot of motion up and down the neck rather than from string to string. It is not the best tuning for playing old standard bass guitar riffs since they were written around fourths, so it may force you to play songs differently which can be either good or bad but always different. It is a good tuning if you want to play string music, I'm still undecided if it will work out well for me in the long run for the "gospel" music I play at church.
Ken
This is not without historical precedent, before even tempered tunings became the norm, keyboard instruments would be tuned to suit a narrow range of keys and would sound wildly out of tune in other keys. Guitars have their frets put in the even tempered locations so no problem with them but the old viola de gamba family of stringed instruments used tied on frets that could be shifted to optimize their locations for a given key. Even today violin family string players will finger notes differently to suit the key they are playing in and they will finger differently when playing a solo than they do when playing in the ensemble.Even if you stick with a "standard" tuning you have valid choices to make. Many will tune their four strings BEAD to pick up the notes between B and E on the bottom string. That is still a standard tuning because it is in fourths. Then there are a few of us who tune a four string CGDA. This is also a standard tuning but it is the violin family standard tuning in fifths. The advantage here is that you get the range of a five string tuned in fourths without the bother of that fifth string! As has been mentioned it will change your familiar patterns and it usually makes them easiest to play on two strings rather than three which can result in a lot of motion up and down the neck rather than from string to string. It is not the best tuning for playing old standard bass guitar riffs since they were written around fourths, so it may force you to play songs differently which can be either good or bad but always different. It is a good tuning if you want to play string music, I'm still undecided if it will work out well for me in the long run for the "gospel" music I play at church.
Ken
