NOTE: I copied this from a website. www.religioustolerance.org Most of this isn't my personal voice but I think this shows some good points in the case of Jonathan and David's relationship.
1 Samuel 18:1-4
"...Jonathan became one in spirit with David and he loved him as himself. From that day, Saul kept David with him and did not let him return to his father's house. And Jonathan made a covenant with David because he loved him as himself. Jonathan took off the robe he was wearing and gave it to David, along with his tunic, and even his sword, his bow and his belt." (NIV)
In those days there wasn't underwear, so Jonathan would have been completely naked in front of David. This was really unusual back then unless their relationship were physical.
1 Samuel 18:20-21
"Now Saul's daughter Michal was in love with David, and when they told Saul about it, he was pleased. 'I will give her to him', he thought, 'so that she may be a snare to him and so that the hand of the Philistines may be against him'. Now you have a second opportunity to become my son-in-law" (NIV)
In the King James Version, the end of Verse 21 reads:
"Thou shalt this day be my son-in-law, in the one of
the twain." (KJV)
Saul's belief was that David would be so distracted by a wife that he would not be an effective fighter and would be killed by the Philistines. He offered first his daughter Merab, but that was rejected, presumably by her. Then he offered Michal. There is an interesting phrase used at the end of verse 21. In both the NIV and KJV, it would seem that David's first opportunity to be a son-in-law was with the older daughter Merab, and his second was with the younger daughter Michal. The KJV preserves the original text in its clearest form; it implies that David would become Saul's son-in-law through "one of the twain." "Twain" means "two", so the verse seems to refer to one of Saul's two daughters. Unfortunately, this is a mistranslation. The underlined phrase "the one of" does not exist in the Hebrew original. The words are shown in italics in the King James Version; this is an admission by the translators that they made the words up. Thus, if the KJV translators had been truly honest, they would have written:
"Thou shalt this day be my son-in-law, in the twain."
In modern English, this might be written: "Today, you are son-in-law with two of my children" That would refer to both his son Jonathan and his daughter Michal.
So there it is. I believe that their relationship probably wasn't sexual, but I do think that David loved Jonathan in a way that was more than a friendship, and vice versa.