Useful Combinations
Fire and Wind
A common combination,where the wind increase the fire's power and strength,by adding oxygen to it.As the wind contains a lot of oxygen,which supports combustion,the result is BOOM!!! The way in which this combination would be used is to first use a relative large fire jutsu,and quickly after,follow it up with a wind jutsu.This can be done at mid range to allow both jutsu to mix,and become an explosive cocktail.This can be done alone if you use kage bunshin,or if you have a summon like Jiraiya had,that can use Katon.A Kakuzu bio would be able to use many combinations effectively due to his masks.
Water and Wind
In this combination,the wind augments the water,by increasing its cutting capability.The wind enhances the speed of the water,making it fast.The water is then able to cut through certain things.This makes an already powerful water jutsu,even more deadly.Imagine a torrent of water,as it hits you with its destructive power,it also cuts you when the wind is added.Truly,a remarkable combo,then can destroy the greatest of opponents.This combo would be awesome,if done with a partner,at a water source.A lot of water plus cutting power equals overkill!!! Can be done using a clone,who will perform the water jutsu and I use the wind jutsu.
Earth and Fire
From what I have seen,earth jutsu can be used to put the opponent in an unescapable dome,and then cooking him alive inside it!! The dome would block in the oxygen,making it like a coffin,then add extreme heat and bam!! you have a cooked shinobi.Not only a dome,but also a tunnel like structure closed at one side and fire from the other.Truly a gruesome technique.Could be used alone if you were to first trap,then cook the opponent.
Fire and Lightning
Never actually seen this before,but let me improvise.The fire could be used as a distraction while you prepare you lightning.So while the opponent is distracted by the fire,you use a quick lightning jutsu right through the fire.As the opponent cant see it,they will be struck OR you use a fire jutsu to press the opponent into a tight corner,then strike them with lightning as they have nowhere to go.This is what I THINK,first time hearing about this combo xD The clone could use the fire jutsu,and I would follow up,using the lightning
Water and Lightning
Also,a well known combo.The user will first use a water jutsu to create a puddle under the enemy,then use a lightning jutsu to electrocute them.Naturally,if you put a live wire containing electricity into water,you would be electrocuted,the same applies here.If you are in contact with the water that becomes charged with lightning,it bye-bye (as stated by NK).Now this combo is truly powerful due to the range in which it travels and its strength.Can be done alone if at a water source,and or use a clone if not.
Neutral Combinations
Earth and Wind
Another weird one.These two elements wont augment each other,if you use an earth jutsu and then in conjuction with a wind jutsu,the earth wont gain any noticeable changes.I could be completely wrong,as I just cant think of a way they would be of any help to each other ._. With a partner or a summon to perform this combo
Ineffective Combinations
Wind and Lightning
Naturally,this combo would be ineffective due to elemental strengths and weaknesses.Lightning is weak against wind,so if used together,it would not make the jutsu stronger.It would probably decrease in terms of rank and power,and also be worthless against a strong opponent.This would be a waste of two of the three jutsu you can perform per turn and would leave you vulnerable,thus making it truly ineffective.
Fire and Water
Another case of elemental strengths and weakness.We all know,fire is weak against water.Using them together would be a total waste of chakra.They would negate and become extremely weak.A very ineffective combo indeed.
Earth and Lightning
Firstly,if used together the lightning would crumble the earth,as it is weak against it.So combining these two,wouldnt make any sense.