Battle of Trafalgar
Observing that some of the leewardmost of the prizes were escaping towards the Spanish coast, Leviathan asked for and was granted permission by Collingwood to try to retrieve the prizes and bring them to anchor. Leviathan chased Monarca, but on 24 October she came across Rayo, dismasted but still flying Spanish colours, at anchor off the shoals of Sanlúcar. At this point the 74 gun HMS Donegal, en route from Gibraltar under Captain Pulteney Malcolm, was seen approaching from the south on the larboard tack with a moderate breeze from northwest-by-north and steered directly for the Spanish three-decker. At about ten o'clock, just as Monarca had got within little more than a mile of Rayo, Leviathan fired a warning shot wide of Monarca, to oblige her to drop anchor. The shot fell between Monarca and Rayo. The latter, conceiving that it was probably intended for her, hauled down her colours, and was taken by HMS Donegal, who anchored alongside and took off the prisoners. Leviathan resumed her pursuit of Monarca, eventually catching up and forcing her to surrender. On boarding her, her British captors found that she was in a sinking state, and so removed the British prize crew, and nearly all of her original Spanish crew members. The nearly empty Monarca parted her cable and was wrecked during the night. Despite the efforts of her British prize crew, Rayo was driven onshore on 26 October and wrecked, with the loss of 25 men. The remainder of the prize crew were made prisoners by the Spanish.

Casualties: 

Aftermath: In the aftermath of the storm, Collingwood wrote:

The condition of our own ships was such that it was very doubtful what would be their fate. Many a time I would have given the whole group of our capture, to ensure our own ... I can only say that in my life I never saw such efforts as were made to save these [prize] ships, and would rather fight another battle than pass through such a week as followed it.
On balance, the allied counter-attack achieved little. In forcing the British to suspend their repairs to defend themselves, it influenced Collingwood's decision to sink or set fire to the most damaged of his remaining prizes. Cosmao retook 2 Spanish ships of the line, but it cost him 1 French and 2 Spanish vessels to do so. Fearing their loss, the British burnt or sank Santísima Trinidad, Argonauta, San Antonio, and Intrépide. Only four of the British prizes, the French Swiftsure and the Spanish Bahama, San Ildefonso and San Juan Nepomuceno survived to be taken to Britain. After the end of the battle and storm only 9 ships of the line were left in Cádiz.
Spanish military garrisons and civilians set out to rescue survivors from the numerous shipwrecks scattered along the Andalusian coast. British prize crews were captured and given good treatment. On 27 October, Collingwood offered the governor of Cádiz to put his Spanish wounded prisoners ashore and set them free. The governor and Gravina offered in exchange to release their British prisoners, who boarded the British fleet. The French later joined this humanitarian agreement.
The disparity in losses has been attributed by some historians less to Nelson's daring tactics than to the difference in fighting readiness of the two fleets. Nelson's fleet was made up of ships of the line which had spent a considerable amount of sea time during the months of blockades of French ports, whilst the French fleet had generally been at anchor in port. However, Villeneuve's fleet had just spent months at sea crossing the Atlantic twice, which supports the proposition that the main difference between the two fleets' combat effectiveness was the morale of the leaders. The daring tactics employed by Nelson were to ensure a strategically decisive result. The results vindicated his naval judgement.

Results: When Rosily arrived in Cádiz, he found only five French ships, rather than the 18 he was expecting. The surviving ships remained bottled up in Cádiz until 1808 when Napoleon invaded Spain. The French ships were then seized by the Spanish forces and put into service against France.
HMS Victory made her way to Gibraltar for repairs, carrying Nelson's body. She put into Rosia Bay, Gibraltar and after emergency repairs were carried out, returned to Britain. Many of the injured crew were taken ashore at Gibraltar and treated in the Naval Hospital. Men who subsequently died from injuries sustained at the battle are buried in or near the Trafalgar Cemetery, at the south end of Main Street, Gibraltar.
One Royal Marine officer, Captain Charles Adair, was killed on board Victory, and Royal Marine Lieutenant Lewis Buckle Reeve was seriously wounded and laid next to Nelson.
The battle took place the day after the Battle of Ulm, and Napoleon did not hear about it for weeks—the Grande Armée had left Boulogne to fight Britain's allies before they could combine their armies. He had tight control over the Paris media and kept the defeat a closely guarded secret for over a month, at which point newspapers proclaimed it to have been a tremendous victory. In a counter-propaganda move, a fabricated text declaring the battle a "spectacular victory" for the French and Spanish was published in Herald and attributed to Le Moniteur Universel.
Vice-Admiral Villeneuve was taken prisoner aboard his flagship and taken back to Britain. After his parole in 1806, he returned to France, where he was found dead in his inn room during a stop on the way to Paris, with six stab wounds in the chest from a dining knife. It was officially recorded that he had committed suicide.
Despite the British victory over the Franco-Spanish navies, Trafalgar had negligible impact on the remainder of the War of the Third Coalition. Less than two months later, Napoleon decisively defeated the Third Coalition at the Battle of Austerlitz, knocking Austria out of the war and forcing the dissolution of the Holy Roman Empire. Although Trafalgar meant France could no longer challenge Britain at sea, Napoleon proceeded to establish the Continental System in an attempt to deny Britain trade with the continent. Further during the War of the Third Coalition, the British Navy would experience defeats in both 1806 and 1807 against the Spanish in the British invasions of the River Plate. The Napoleonic Wars continued for another ten years after Trafalgar.
Nelson's body was preserved in a barrel of brandy for the trip home to a hero's funeral.

Consequences: Following the battle, the Royal Navy was never again seriously challenged by the French fleet in a large-scale engagement. Napoleon had already abandoned his plans of invasion before the battle and they were never revived. The battle did not mean, however, that the French naval challenge to Britain was over. First, as the French control over the continent expanded, Britain had to take active steps with the Battle of Copenhagen in 1807 and elsewhere in 1808 to prevent the ships of smaller European navies from falling into French hands. This effort was largely successful, but did not end the French threat as Napoleon instituted a large-scale shipbuilding programme that had produced a fleet of 80 ships of the line at the time of his fall from power in 1814, with more under construction. However, despite constituting a substantial fleet in being, these had no impact on Britain's naval superiority throughout the conflict. For almost 10 years after Trafalgar, the Royal Navy maintained a close blockade of French bases and observed the growth of the French fleet. In the end, Napoleon's Empire was destroyed by land before his ambitious naval build-up could be completed. The next naval battles between the British and Spanish would be the British Invasions of the River Plate in 1806 and 1807, where the British Navy would fail to capture Viceroyalty of the Rio de la Plata.
The Royal Navy proceeded to dominate the sea until the Second World War. Although the victory at Trafalgar was typically given as the reason at the time, modern historical analyses suggest that relative economic strength was an important underlying cause of British naval mastery.

Nelson became – and remains – Britain's greatest naval war hero, and an inspiration to the Royal Navy, yet his unorthodox tactics were seldom emulated by later generations. The first monument to be erected in Britain to commemorate Nelson may be that raised on Glasgow Green in 1806, albeit possibly preceded by a monument at Taynuilt, near Oban in Scotland dated 1805, both also commemorating the many Scots crew and captains at the battle. The 144-foot-tall (44 m) Nelson Monument on Glasgow Green was designed by David Hamilton and paid for by public subscription. Around the base are the names of his major victories: Aboukir (1798), Copenhagen (1801) and Trafalgar (1805). The Nelson Monument overlooking Portsmouth was built in 1807–08 with money subscribed by sailors and marines who served at Trafalgar. In 1808, Nelson's Pillar was erected by leading members of the Anglo-Irish aristocracy in Dublin to commemorate Nelson and his achievements (between 10% and 20% of the sailors at Trafalgar had been from Ireland), and remained until it was destroyed in a bombing by "Old IRA" members in 1966.