At the moment, Britain is ranked 5th in the world, in terms of overall military strength and it is world renowned.
Active military personnel number 121,000. Reserve military personell 129,500.
The British army also has the second best GPP, or Global Power Projection capability, which means is can go anywhere in the world at a moments notice. What gives the Army the edge is its special forces. The SAS, or Special Air Service, is world renowned, and has be longest training and the harshest in the world. It is generally accepted that it is the best in the world. Even the Americans used the SAS instead of their own special forces to rescue at CIA hostage. The SBS, or Special Boat Service, is also world renowned.
Note that these two special forces units were the first to be started in the world, too. The British army also has access to satellites and has its own Secret Intelligence agency called DI, or Defense Intelligence which acts in accordance with MI6 (they handle international security and conduct covert operations abroad), MI5 (deals with national and internal security and counter terrorists and GCHQ (Britain's NSA, or basically the agency which listens to everyone's calls).
Technology/Vehicles/Tanks
The British army uses the Challenger 2 tank, which is considered to be one of the best in the world, as well as the Apache attack heli, which is also used by the US Army, and is also one of the best available. The British army uses drones, too. For example their Reaper drones are probably the best in the world. They are also developing the BAES Taranis drone, which will surpass the United States in both stealth and overall damage on the enemy. It will be able to cross the Atlantic Ocean and select its own targets.
Training
As mentioned before, the British Army has the longest training time in the world as well as the harshest, for both regular, and special forces.
Weapons
Britain uses the assault rifle LA85A2, or the HK SA80. It used to be simply useless, but then Heckler and Kotch, an arms manufacturer, fixed the problem. This rifle is now the most expensive in the world, and is for definite, one of the best ever made.
Famous battles/notable battles won.
The British army has seen combat since the 1700s, but your question was about the current army. Britain's SAS and SBS have rescued many hostages, notable in Nigeria, as will as in the Iranian Embassy seige. Britain has seen action recently in Iraq, Afghanistan and will inevitably be involved in counter-terrorism operations in Northern Africa.
Generally speaking, a standing army in the view of economist Adam Smith was an economic drain on Great Britain. He also said that in order to protect British society from invasion, the upkeep of a strong army and navy was required.
P. H. Smitherman has written: 'Cavalry uniforms of the British Army' -- subject(s): Great Britain, Great Britain. Army. Cavalry, Uniforms 'Uniforms of the Royal Artillery 1716-1966' -- subject(s): Great Britain, Great Britain. Army. Royal Artillery, Great Britain. Army. Royal Regiment of Artillery, Uniforms 'Uniforms of the Scottish regiments' -- subject(s): Great Britain, Great Britain. Army, Scottish regiments, Uniforms
Britain obviously
God and his army of demons NEW RESPONDENT. Great Britain.
Michael Barthorp has written: 'To face the daring Maoris' -- subject(s): Great Britain, Great Britain. Army, History, New Zealand Maori War, 1845-1847 'The Northamptonshire Regiment' -- subject(s): Great Britain, Great Britain. Army. Northamptonshire Regiment 'The Jacobite Rebellions 1689-1745' 'The British Army on Campaign (1), 1816-1853' 'The British Army on Campaign (4)' 'Heroes of the Crimea' -- subject(s): Balaklava, Battle of, Balaklava, Ukraine, 1854, Inkerman, Battle of, Ukraine, 1854 'Crimean uniforms' -- subject(s): Crimean War, 1853-1856, Great Britain, Great Britain. Army, Great Britain. Army. Infantry, Uniforms 'The Old Contemptibles' 'Wellington's generals' -- subject(s): Biography, Generals, Great Britain, Great Britain. Army, Military leadership, Relations with generals 'Napoleon's Egyptian Campaigns 1798-1801' 'British army on campaign 1816-1902' -- subject(s): Great Britain, Great Britain. Army, History, Military History 'The Jacobite Rebellions' 'British cavalry uniforms since 1660' -- subject(s): Cavalry, Great Britain, Great Britain. Army, History, Uniforms
John Biddulph has written: 'The Nineteenth and their times' -- subject(s): Accessible book, Great Britain. Army. Cavalry. 23rd Light Dragoons, 1781-1786, Great Britain. Army. Cavalry. 19th Regiment, 1759-1763, Great Britain. Army. Cavalry. 19th Light Dragoons, 1786-1821, Great Britain, Great Britain. Army. Cavalry. 19th Regiment, 1779-1783, British Regimental histories, Great Britain. Army. Cavalry. 19th Hussars, 1858-, History
Mike Curtis has written: 'CQB' -- subject(s): Biography, Commando troops, Great Britain, Great Britain. Army, Great Britain. Army. Special Air Service
John MacKay has written: 'An old Scots brigade' -- subject(s): Great Britain, Great Britain. Army. Mackay's Regiment, Great Britain. Army. Royal Scots
C. T. Atkinson has written: 'The Royal Hampshire Regiment' -- subject(s): Great Britain, Great Britain. Army. Hampshire Regiment 'The history of the South Wales Borderers, 1914-1918' -- subject(s): Great Britain, Great Britain. Army. South Wales Borderers 'The Dorsetshire regiment' -- subject(s): Great Britain, Great Britain. Army. Dorsetshire Regiment 'The Seventh Division 1914-1918' -- subject(s): Armies, Organization 'The Devonshire Regiment 1914-1918' -- subject(s): Great Britain, Great Britain. Army. Devonshire Regiment
The Continental Army was the group that the colonies organized to fight against Great Britain.
Gerald Edmund Boyle has written: 'The Rifle Brigade century' -- subject(s): Great Britain, Great Britain. Army, Great Britain. Army. Rifle Brigade, Registers
Henry M. Lawson has written: 'Our army of the future' -- subject(s): Decentralization in management, Great Britain, Great Britain. Army, Great Britain. War Office, Management