So far there have been three HMS Sheffield
s, each one serving as a cruiser-sized vessel for the Royal Navy
The first one was a Southampton Class light cruiser which served from 1937 until 1967, outlasting the other four Southampton Class ships - the Birmingham, the Glasgow, the Newcastle and the Southampton itself. Of the lot, the Southampton was damaged by Stukas and sunk in 1941, whilst the others served their time in WW2 before being scrapped. The Sheffield was armed with 12 6.0 inch guns and participated in the hunt for the Bismark. Due to an unfortunate misunderstanding the Ark Royal tried to sink it with Fairey Swordfish torpedo bombers; luckily for the Sheffield, the magnetic fuses in the torpedoes didn't work properly, and an embarrasing faux-pas was averted (as were the deaths of 930 crewmembers).
The next HMS Sheffield was not so fortunate. A Type 42 Destroyer, it was launched in 1971 and cost £23 million. Type 42 destroyers were designed for air defence, and 12 were built in total - plus, ironically, two for the Argentine navy. Armed with a Lynx helicopter and the Sea Dart missile system, the Type 42s were designed to engage the Soviet juggernaut, presumably buying time with the lives of their 300-odd crew for American reinforcements to arrive in the event of World War III.
As things turned out, the Sheffield was sent into action in the Falklands War in 1982. The Sea Dart system was designed primarily to engage incoming Soviet bombers, and wasn't nearly as effective against low-level fighter aircraft (for which the Type 42 relied on backup from the Sea Wolf system on an escorting Type 22). On May the 4th, two days after the sinking of the General Belgrano, and four years to the day after the Conservative election victory of 1979, the Sheffield was hit by an Exocet missile. The missile didn't explode, but fires broke out, gutting the ship and causing the deaths of 21 sailors and the incendiary injuries of scores more.
It was the first loss the Royal Navy had experienced to enemy fire since World War 2. Although British soldiers had been killed in Northern Ireland, Cyprus and a variety of colonial wars, this was still a major shock. The deserted destroyer eventually sank on the 10th of May whilst under tow. Of the other two Type 42 destroyers sent to the Falklands, the Coventry was also sunk (with the loss of 19 lives) whilst the Glasgow was damaged and sent back home. Controversy still simmers as to the sinking of the Sheffield - there are allegations that key members of staff were absent from the operations room at the time of the sinking. Furthermore, the war was not a great advertisement for the Type 42 destroyer.
Whilst the surviving Type 42 destroyers remain in RN service (where they will stay until at least 2007), a new HMS Sheffield was launched in 1986. It's a Type 22 Broadsword Class frigate. HMS Broadsword and its ilk served in the Falklands and were more successful than the Type 42s, with no losses, and are used nowadays as a multi-role anti-submarine, anti-air defence platform. Another Type 22 frigate is named after HMS Coventry, a ship which was sunk whilst defending HMS Broadsword from attack by Argentine A4 Skyhawks.