After the American Revolution, the British army saw how effective the rifle was in battle. An experimental corps was drawn up (I believe called the Experimental Corps of Rifles) and was deemed a success. The corps then became the Rifle Brigade, which saw action in South America, where they were heavily praised by the the General commanding the siege of Montevideo.

During the Peninsula war and following Waterloo campaign, the 95th distinguished themselves on several occasions. It was during this time the regiment became famous and incredibly popular, which led to an additional battalion being raised. The Rifles (specifically the 60th) were mentioned in despatches for Talavera, but also notably performed at Sabugal, forcing a 10,000 French force back while being heavily outnumbered. Other acts of bravery occurred towards the end of the campaign with regiments being used to great success in capture forts and cover retreats.

I also recall a soldiers anecdote (a quick search proved my recollection to be correct) where a rifleman shot an officer beyond 200 metres (some say up to 600). He was then told this was a fluke, so proceeded to shoot a second officer who went to his aid. Bare in mind that muskets were mostly ineffective beyond 40 metres or so.

It's also worth noting that the Rifles didn't just comprise of British units - there was also a Portuguese regiment that fought alongside them.

Mark Urban wrote a fantastic book, Rifles, covering the 95th during the Napoleonic Wars and goes into great detail of the battles they fought in. I cannot recommend that book more as the level of detail is incredible. I would also recommend having a look through some of the soldiers memoirs as that's where Mark finds his sources.