Oh yes they're still around. They are actually still royalty but only in Spain and Luxembourg. The Luxembourg line is descended from the former Dukes of the Italian state of Parma. In Spain, they took power after the War of Spanish Succession and broke away from the French line. While Spain was a republic, then ruled by Amadeo from the House of Savoy, and almost a Hohenzollern which further deteriorated relations between France and Prussia. After the republic and dictatorship the Bourbons once again were rulers of Spain as constitutional monarchs as they were before the Republicans. If you are inquiring about the French branch, they are still around and occasionally lobby for monarchism. Actually the current claimant that the Bonapartes should have the nonexistent Throne of France is from a Bourbon mother. Many noble houses are still around they just don't sit on any thrones. Many people are just non-noble descendants as well. I'm technically descended from King John, a Plantagenet, but I'm just a standard middle class American. The British maintain a massive list of succession for the throne that includes all relatives of Sophia the Electress of Hanover. Last in line is a middle class German woman.

Louis Alphonse, Duke of Anjou is the current head of the house of Bourbon and claimant to the throne of France as the pretender King Louis XX. He is also (via his mother) the great grandson of Francisco Franco and is the first cousin once removed of the current King of Spain. He is married to a commoner and they have three children, the second of whom was a boy and consequently is the pretender dauphin. You can read more about Louis XX here: http://en.wikipedia.org/wiki/Louis_Alphonse,_Duke_of_Anjou

This family indeed still exists.
First, one must remember that France definitely turned to a republic only in 1870 (with the 3rd republic): there have been 2 republics, 4 kings and 2 emperors between 1792 and 1870 (if one count only those who ruled for more than a few hours).
As it was pointed out, the current king of Spain is a member of this house. It can be argued that he should be considered as the head of this house and pretendant to the French throne (after the Spanish succession war, a grandson of Louis XIV, Philippe V, gained the spanish throne: the current king of Spain is his descendant. To gain this throne, Philippe V renounced the french throne in the treaty of Utrecht in 1713, but the crown is not a property of the king, and Charles V may not have had the right to renounce it). This is the legitimist view.
Now, it is argued that a foreigner prince can not reach the throne, and acknowledge the treaty of Utrecht. After the first empire and Npoleon defeat, two brothers of Louis XVI accessed to the throne. Louis Philippe I then accessed the throne; he was a cousin of Louis XVI, and the Orleans branch is descended from him. The descendants of Charles X and Louis Phillippe lived in Austria and in the UK till the 20th century. A grandson of Charles X (Henri) actually had an opportunity to access the throne in 1870.
Now it turns hard : Louis-Phillippe father, Louis-Egalité, voted for the death of Louis XVI (he was elected in the convention... and even the hawkish revolutionaries found this vote disgusting); he could be considered as a kingslayer, thus excluding him and his descendants from the throne; the spanish branch is excluded thanks to the treaty of Utrecht; Henri had no descendants. And the Bourbon-Anjou house should have gained the throne after Henri's death if the Utrecht treaty is valid.

There are many people descended from the last kings of France (a more or less complete list can be found here :http://en.wikipedia.org/wiki/List_of_living_legitimate_male_Capetians ). And no one agrees on which of them should have the throne should France turn back to a monarchy.
PS: the descendants of Napoleon III "wants" this throne too.....