Here were some suitors to Elizabeth I. A lot of these were even before she was Queen. I have highlighted these in blue. Most of these were to gain or maintain (Sir Thomas Seymour) power in England.

1534 Duke of Angoulme (third son of Francis I)
1544 Prince Philip of Spain (King Philip II)
1547 Sir Thomas Seymour
1553 Edward Courtenay
1554 Emanuel Philibert, Duke of Savoy
1554 Prince Frederick of Denmark
1556 Prince Eric of Sweden
1556 Don Carlos (son of King Philip II)
1559 King Philip II
1559 Sir William Pickering
1559 James Hamilton, Earl of Arran
1559 Henry Fitzalan, Earl of Arundel
1559 Lord Robert Dudley
1560 King Eric XVI of Sweden
1560 Duke of Holstein
1560 King Charles IX of France
1560 Henry de Valois, Duke of Anjou
1563 Lord Darnley
1568 Archduke Charles of Austria
1570 Henry Duke of Anjou
1572 Francois, Duke of Alencon

Elizabeth had to marry someone powerful who was the same religion of her, Protestant. She strongly considered...

      Eric of Sweden

      Lord Robert Dudley

Lord Darnley

      Archduke Charles

In the end, Elizabeth never married.
  
I got this information from
http://www.elizabethan-era.org.uk/suitors-of-queen-elizabeth-i.htm.