Although opposition from the Jacobites arose immediately following the James' deposition in 1688 and recurred throughout the first half of the 18th century, only two major "rebellions" are normally recognised by this title: the '15 and the '45. However, the Jacobite uprising of 1689 -- see Battle of Killiecrankie -- is also sometimes included in this category.
The first of the two major "rebellions", in 1715, occurred not long after the accession of King George I, its purpose being to place James II's son, James Francis Edward Stuart, the Old Pretender, on the throne. It was raised by the disgruntled Earl of Mar, Bobbin' John, in response to having his attempts to gain office in the incoming Hanoverian government rebuffed. It was organised without reference to the Stuarts in France who were not prepared for it. The Old Pretender's arrival in Britain was delayed by illness, and he was unable to take advantage of the initiative taken by his followers.
The second "rebellion", in 1745, was led by James II's grandson, Bonnie Prince Charlie (though his father was still alive), and came close to overturning the status quo and placing the Stuarts back on the throne. After the fiasco of the Battle of Culloden, the Jacobites never again had a serious opportunity of military success.
more detail about the events of 1689, 1715 and 1745 to be added
