This is such a tough question and there are many different schools of thought on it. Some historians point out that there was no evidence that Elizabeth slept with Robert Dudley or any of her favourites and that when spies (from ambassadors) questioned her ladies and investigated the rumours about Elizabeth's behaviour all they found was rumour and scandal, no proof of any sexual misconduct.
Some people also point out that Elizabeth would surely have become pregnant if she had slept with Dudley, but then there was basic contraception around or Elizabeth could have been barren, but would she really have taken this risk? Plus she was never really alone, she was constantly supervised by advisers and her ladies - how could she have got away with it.
Other people believe that there was just too much rumour for nothing to have gone on!
But I for one believe that Elizabeth died a virgin. I believe that she was a passionate woman and that she fell in love a few times but that she always put her country first and saw herself as married to England, she could not risk her country for a man.
Weir points out that Elizabeth "may have made the equation that sexual involvement was inextricably linked with death" - after all, her mother had been executed for adultery, her stepmother Catherine Howard had been executed for adultery, her stepmother Catherine Parr died after giving birth, and her first love Thomas Seymour (or abuser!) was executed. That might put your off sex! The idea of childbirth may also have scared her and put her off the idea of sexual involvement - Her grandmother Elizabeth of York had died of puerperal fever, as had Jane Seymour and Catherine Parr. Sex inevitably could lead to childbirth and, in those days, childbirth was a risky business.
Elizabeth may also have had physical problems that could have stopped her having sex. Weir, in her book "Elizabeth the Queen", writes of how the playwright Ben Jonson had talked of Elizabeth having "a membrane on her which made her incapable of man", meaning either an abnormally thick hymen or perhaps Elizabeth may have suffered from Vaginismus, a condition which affects a woman's ability to have sex because of a tightness of the vaginal muscles. Weir also makes the point that although there were scandals and rumours because of Elizabeth's fondness of men and flirting, "Elizabeth was too much mistress of herself and too great a stateswoman to succumb to the temptations of illicit sex". She just would not have risked her status, reputation or throne in that way.