I've wondered this for a while now; the Hapsburgs were involved in numerous royal families over the European Middle Ages and later, and though I know very little about them, I can't help but wonder if the family went to war with itself while ruling other countries or kingdoms.
Please pardon if I sound like a dolt; the politics of royal families in Medieval Europe are something I know almost nothing about.
The Habsburgs mainly ruled in two places: Austria/the Holy Roman Empire and Spain. When the two branches divided in the 16th century, the Austrian (also called the Habsburg Monarchy or the Danubian Monarchy) was the Junior branch, and the Spanish Hapsburgs were the senior branch. The two branches split in 1521 when Holy Roman Emperor Charles V (aka King Charles I of Spain) assigned his brother Ferdinand the Austrian lands (the Spanish lands being, by this point, the more important and valuable of the Hapsburgs domains). The Spanish Hapsburgs died out in 1700 (prompting the War of Spanish Succession, which the Bourbons eventually won), and the Austrian Branch technically died out in 1780 (the male line died out in 1740, prompting the War of Austrian Succession), and was replaced officially by the House of Habsburgs-Lorraine (so one of the members of the House of Lorraine had married a female Habsburg). This continued to be known as House of Habsburg, especially in common speech. By 1806, the Holy Roman Empire was a less and less politically meaningful entity and the Habsburg(-Lorraine) Holy Roman Emperor Francis II, in anticipation of the Napoleonic Wars, declared himself Francis I, Emperor of Austria (rather than the HRE). This line ruled the Austrian Empire (after 1867, Austria-Hungary, as a personal union between the Austrian Empire and the Kingdom of Hungary) until 1918 and there are still lines of this family that are alive and kicking.
But really, we only have the period from 1521 to 1700 where there were two important Habsburgs ruling two important places. I am not aware of any war fought between them. The exact relationships between the the lines was complex. Ferdinand the I originally ruled in the name of his brother, but then later was elected King of Hungary and Bohemia in his own right, and Charles V only officially divided the two hereditary lines with his abdication in 1556, where he officially gave his brother younger brother Ferdinand the "Habsburg Monarchy" Austrian lands (Ferdinand also succeed him as HRE), and his son Philip II the Spanish Empire which included not just Spain, but also the former lands of the Burgundian Dynasty like the Low Countries as well as Southern Italy (and officially Jerusalem). Charles V was the scion to three important European dynasties (and several minor ones): the House of Habsburg, who were Holy Roman Emperors; the House of Valois-Burgundy, who controlled the Low Countries; and the House of Trastámara, who controlled the Crowns of Castille and Aragon. The Habsburgs, incidentally, came to get such power not through war-making but through really excellent, strategic marriages that I will openly admit to not fully understanding.
Anyway, the two branches signed a secret treaty in 1617, which I again don't know very much about (I know Habsburg history primarily through Austrian history), but it was called the Oñate treaty. This was occasioned because the main branch of Austrian Habsburgs had died childless, and they were transferring his claims to yet another branch of the family, and hoped the Spanish Habsburgs wouldn't claim it back. But basically, they were generally on the same side as many of the wars of this period were religious ones or wars of succession--they settled their succession disputes peacefully, and were on the same (Catholic) side of the religious contests. The Spanish Crown was mainly interested in keeping the rebellious (and increasingly Protestant) Netherlands, while Austria was mainly worried about fights within and around the HRE.
It depends on your definition of war. Is a feud between two counties/dukes/archdukes a war?
They always quarreled with one another, being a numerous family. I shall give two examples. One is a new one, the other expands on /u/yodatsracist 's mentioning of the Oñate treaty.
For instance, in 1308, Johann, the duke of Swabia, Austria and Steyer, murdered his uncle, Albrecht I, King of the Romans and count of Habsburg (the territory in Aargau), during a quarrel caused by Albrecht holding back an inheritance (the regentship of Swabia). He was consequently called Johann Parricida. He got banned by the next King of the Romans and disappeared.
There was a lot of inheritance fighting among German families in the Middle Age until even after the Thirty-years-War, caused by the German inheritance laws. The lands of the Habsburgs were splitted numerous times, sometimes they fought, sometimes they just quarreled.
Another instance, this time bloodshed nearly was avoided: Rudolf II., the emperor, refused to marry or to name his brother as his heir. This weakened the position of the Habsburgs. So Matthias, the brother, who was, among other things, King of Hungary, conspired with their other brother, Maximilian, who was the Grandmaster of the Teutonic Order, and their cousin, Ferdinand, who was regent of Inner Austria, to have the emperor declared insane.
This didn't work, and Matthias assembled an army and marched on Prague. Rudolf saw how bad things stood. However, the conspiritors also couldn't bring all of the regional parlaments on their side, and they had to compromise. But now, the brother of Ferdinand, Leopold, saw his chance and invaded Bohemia with mercenaries, who were originally raised by Rudolf, to have him crowned King of Bohemia. These mercenaries occupied Prague, but fled when Matthias came with his army. Matthias was crowned King of Bohemia in 1611. When Rudolf, who was now powerless, died one year later, Matthias was elected emperor.
In a cruel twist of fate, Matthias had more or less the same problems as Rudolf. Heirless, he had, after a lot of intrige and the involvement of two of his other cousins, to make Ferdinand King of Bohemia in 1617. Ferdinand in turn had to compromise with his kinsman, Philip III. of Spain, when Philip tried to get the crown of Hungary, in the Oñate treaty.
And this is only a small piece of the mosaic that lead to the Thirty-years-War, starting one year later.
Side question: can anybody recommend a good podcast or documentary about the Hapsburgs?
A bit off-topic but I've seen people misspelling Habsburg as Hapsburg and I'm wondering where this misconception originated and whether it's limited to English-speaking countries.