Why is the Queen's husband not King?
One becomes monarch only by blood. A man who marries a Queen can never become King, and is known instead as the Prince consort.
A woman who marries the King is given the title of Queen, but in truth she can never rule as monarch. If the King dies before the Queen, she can't rule but her children can ascend the throne. If she doesn't have living children, some other branch of the King's family—related by blood—inherits.
The current Queen, Elizabeth II, descends directly from Alfred the Great, who ruled England 1,140 years ago.
Here are some of the rules that govern who can inherit the British throne:
Because Edward VIII never had any children, Elizabeth would still have become Queen even if Edward had not abdicated when he married Wallis Simpson.
Can Camilla become Queen?
Yes. Camilla will become Queen when Charles becomes King. Normally, she would currently hold the title of Princess of Wales (just as Charles is the Prince of Wales), but she instead took the title of Duchess of Cornwall out of sensitivity for the death of Diana.
Incidentally, Camilla's great-grandmother was Edward VII's mistress. (Edward VII was Charles' great-great-grandfather.)
Kate Middleton will not be the first commoner to marry the heir the the throne. Elizabeth Woodville, who married Edward IV in 1464, and Anne Boleyn, who married Henry VIII in 1533, were both commoners.
Of course, Henry had Anne Boleyn executed in 1536, after Cromwell (probably) engineered accusations of adultery, incest, and treason.
Who currently stands to inherit the throne?
The current Queen is Elizabeth II. Her eldest son, Prince Charles, is first in line to succeed her. The next in line (if Charles dies or abdicates) is Charle's oldest son, Prince William.
A Wikipedia article fully describes the succession to the British throne.