1. William I
2. Henry I
3. Empress Matilda (Maud)
4. Henry II
6. Henry III
7. Edward I
8. Edward II
9. Edward III
10. Lionel of Antwerp, Duke of Clarence
11. Philippa of Ulster
12. Roger Mortimer, Earl of March
13. Anne Mortimer
14. Richard Plantagenet, Duke of York
15. Edward IV
16. Elizabeth of York (wife of Henry VII)
17. Margaret Tudor
18. James V of Scotland
19. Mary, Queen of Scots
20. James I
21. Elizabeth Stuart, Electress Palatine
22. Sophia, Electress of Hanover
23. George I
24. George II
25. Frederick, Prince of Wales
26. George III
27. Prince Edward Augustus
29. Edward VII
30. George V
31. George VI
32. Elizabeth II
(Cribbed in it's entirety from the Answers.com page referenced above)
Everyone on the list is the son or daughter of the person above. Due to some lines becoming extinct (Lancaster, Stewart, Tudor) and other reasons, this is of course very different to the line of succession.
Well, so far so good. But wait; genealogy goes back further than this. As you might imagine, Elizabeth II is able to trace her lineage back, through William I to Charlemagne. Keeping the same generational numbering as before:
-9. CharlemagneSo here we have an answer to the question what makes a royal or noble house noble? It's that (for example) 41 generations ago, one of your ancestors was the Emperor in the West, Heir to the Caesars, Anointed by the Pope, the Holy Roman Emperor Charlemagne.
-8. Pippin of Italy
-7. Bernard of Italy
-6. Pepin, Count of Vermandois
-5. Herbert I, Count of Vermandois
-4. Berengar of Bayeux
-3. Judicael Berengar
-2. Conan I, Duke of Brittany 
-1. Judith of Brittany
0. Robert II, Duke of Normandy
1. William I
But just one cottonpickin' minute! Charlemagne's dynasty, the Carolingians, traced themselves back to the previous Frankish ruling dynasty, the Merovingians. Here, the records get a little dubious; the link between the Carolingians and the Merovingians may have been documented much later than the actual events. Nevertheless, here's the line of descent:
-20. Childeric I
-19. Clovis I
-18. Theodoric I
-17. Theudebert I
-15. Grimwald of Aquitaine
-12. Pippin the Fat
-11. Charles Martel (illegitimate)
-10. Pippin the Short
All well and good; we've traced the descent back to the legendary 5th century founder of the Merovingian dynasty, Merovig (sometimes Merovich). Still more interesting though is Merovig's parentage; his mother was the queen of the Franks, married to Pharamond. However it seems that she became pregnant after swimming in the sea, where she met a sea monster; specifically a Quinotaur, which is a shapechanging creature that is half-bull and half-fish .
Let's put it like this: if you can't trace your family tree back to sea monster, a Norse god or, at least an old style semi-legendary saint, then I'm not interested in your claims of nobility.
 aka the Conqueror. Before that, he was known as William the Bastard, which to me gives all the encouragement he needed to do something that would make history remember him for, other than the questions over his parentage (which are more obscure and interesting than you might think, but that's for another post).
 Which is not quite the achievement you might think; basically every old noble family from west of the Vistula (and many from east of it) can trace themselves back to Charlemagne. That's what being noble is all about.
 No, really. We haven't yet got to the unlikely bit.
 In this example, actually more than one, but lets not go there.
 Holy Blood and Holy Grail, which was not ripped off of by The Da Vinci Code suggests that the Merovingian kings were the descendants of Christ, one symbol for whom was the fish.
 Alfred the Great, who is also an ancestor of the Queen, was a descendant of Odin.