Sonic the hedgehog is an anthropomorphic hedgehog developed by team Sonic for Sega. In plain words, he is a blue hedgehog who acts like a human being - stands on two feet, has gloved hands, wears shoes - the works basically. He is fast and he is very impatient. I mean really impatient. If you don't believe me, show me one place in the game where he stands still and I mean absolutely still.
Knuckles, is the last of his race and is an Echidna. Not much explanation is offered beyond that except how he gets his name. He has two spikes jutting out of each of his hands, with which he fights. Now he is a very formidable enemy and is in charge of guarding the treasure of his tribe. He lives on the Floating Island that has the Chaos Emeralds and the also the Master Emerald. These are magical items that have a lot of power, especially the Master Emerald that is responsible for making the entire island float.
Now, when you are charged with guarding such items and you are the last of your race, things do get tensed around you. So the slightest suggestion that someone might be 'trying' to steal your precious treasure is likely to set you on a fighting spree.
That is what usually happens between Sonic and Knuckles. Sonic actually never intends to steal the Emeralds. But Robotnik usually has a dastardly plan up his sleeve that involves convincing the poor Echidna that Sonic is after his precious Emeralds. Robotnik is actually the one trying to steal them but when it is a video game, you do not get to ask too many uncomfortable questions.
It is understandable that Knuckles would be all suspicious and hyper about his emeralds, enough to overlook who's actually trying to steal them. But thankfully he is not foolish. He does fight Sonic because Robotnik has duped him but he also joins forces with the real Sonic to fight against Robotnik. He seems to harbor no hatred for Sonic on the long term and it is probably just his paranoia regarding his precious gems.
So over all, Sonic and Knuckles have had a love and hate relationship so far. They have fought each other because of Robotnik and worked with each other to bring down Robotnik. In the end, they do make a great fighting duo and a force to reckon with.
This brings the possibility of a solid friendship to the mind but the Echidna is too religious about his duties to entertain such thoughts. Knuckles is a very focused person with just one goal in life (or so it seems) and that is to protect Angel Island from destruction. That includes protecting the Chaos Emeralds and the much sought after Master Emerald at all costs.
Sadly for a lot of fans, this cost seems to be in the form of a constant paranoia on the Echidna's part. However, it really is a treat when Sonic and Knuckles work together. May be it is the rarity that makes it so special.