The short answer is, "We don't know." The text is unclear and we don't have a window onto typical same-gendered relationships of the time. There are several texts that people refer to on this issue:
"When David had finished speaking to Saul, the soul of Jonathan was bound to the soul of David, and Jonathan loved him as his own soul. Saul took him that day and would not let him return to his father’s house. Then Jonathan made a covenant with David, because he loved him as his own soul. Jonathan stripped himself of the robe that he was wearing, and gave it to David, and his armor, and even his sword and his bow and his belt." (1 Sam 18:1-4)
"As soon as the boy had gone, David rose from beside the stone heap and prostrated himself with his face to the ground. He bowed three times, and they kissed each other, and wept with each other; David wept the more. Then Jonathan said to David, “Go in peace, since both of us have sworn in the name of the LORD, saying, ‘The LORD shall be between me and you, and between my descendants and your descendants, forever.’” He got up and left; and Jonathan went into the city. (1 Sam 20:41-42)
"I am distressed for you, my brother Jonathan; greatly beloved were you to me; your love to me was wonderful, passing the love of women." (2 Sam 1:26)
In Jonathan Loved David, author Tom Horner suggests that an unbiased reading of the story indicates a homoerotic relationship. However, the problem is that texts cannot be read in an unbiased manner. We ALWAYS bring our hopes, dreams and expectations to a text when we engage it. I will admit that from the vantage point of a 21st-century American, whose culture is obsessed with sex in general and is coming to grips with homosexuality, the text reads pretty erotic. However, note the context of the reader. When Americans see men holding hands or kissing on the mouth, we usually jump to a homoerotic interpretation whether we are "pro" or "anti" gay. In other cultures, hand-holding or kissing as a greeting are normal activities by men and are not seen as homoerotic. There is no evidence in the history of Biblical interpretation that Jewish or Christian commentators have ever interpreted the relationship between Jonathan and David as being sexual, so I tend to chalk this impression up to our modern, sexually-obsessed culture. When my Old Testament professor, Ellen Davis, was asked about this issue, she said (to paraphrase), "I think it says as much about our devaluation of friendship between men as it does about our obsession with sex."
Indeed, throughout history you find descriptions of the brotherly love between men in flowery terms from Gilgamesh and Enkidu to the Inklings. It's not uncommon to hear people talk about "Marrying their Best Friend" these days, but it used to be rare for husbands and wives to really be "close" in friendly terms. Men were expected to form close bonds with other men in war and work, and such bonds have been written about in poetry and prose. One of the most interesting stories in the history of the Inklings was how C.S. Lewis' marriage to Joy Davidson brought up serious feelings of jealousy in JRR Tolkien. This was probably because Davidson was not only becoming Lewis' wife, but was fulfilling part of his life as a friend that Tolkien had previously held. You can also see such love in the bonds formed between veterans. Watch Band of Brothers sometime. So while Jonathan and David's relationship COULD have been sexual, I think there are many non-sexual male relationships in history that could be described as "wonderful, passing the love of women."
So does that mean that Jonathan and David have no value to the GLBT community as role models? Not unless you buy into the American cultural premise that relationship is all about sex. What is definitely modeled in the story without any stretch of the narrative is a close, loving relationship between two people of the same sex. The language is beautiful and the drama is palpable. We tend to want to drive a wedge between friendship and romance, but I think we have to admit that such a division is a bit artificial and often unhelpful. In many ways, I think the story is more helpful to heterosexuals in helping us get over our homophobic fears of "getting too close" to someone of the same sex.
David loved Jonathan, and Jonathan loved David. I'm not sure much needs to be said beyond that....