The last time swords were used in anger by a regular military force was probably when the crew of the British destroyer HMS Cossack boarded the German freigher Altmark in Norwegian Waters on the 16th of February 1940. Parts of the British boarding party was equipped with cutlasses that werre used during the boarding.

The Swedish Carolean army equipped every man with a rapier and infantry hangers continued to be common side arms of line infantry throughout the 18th and 19th century. Towards the end of the 19th century, most infantry hangers had been replaced by fascine knives that were a kind of a mix between a tool (like a machete) and a short sword, so I am not sure it should count as a sword.

Cavalry continued to use sabres as regular equipment at least until the end of ww2.

15th century plate armour pretty much made swords obselete - if you wished to harm a man clad in plate armour, you used a polearm, an axe, a fighting pick (or crow's beak as they were also called) or a war mace. As gunpowder weapons became better and more common, plate armour declined. Plate armour that covered the entire body and could protect against musketballs became heavy and prohibitively expensive. Only elite cavalry, such as the Imperial Cuirassiers during the 30 years' war, the French Royal Gendarmes or the Polish Winges Hussars could afford it. Other nations would rather have Another cavalryman than a fully armoured one.

That said, cuirasses and helmets prevailed for a long time, especially as they could protect vital areas against cavalry swords, pike points and at times pistolballs. Cavalry wearing cuirasses and helmets prevailed up to ww1.

Swords all but disappeared from the infantry (but always remained with the cavalry) except for two-handed swords (the famous Swiss and German zweihändermänner intended to disrupt the enemy pike-line). When armour declined, swords such as infantry hangers or infantry cutlasses (or rapiers with the Swedish Carolean army) made a return, but only as secondary side arms.

Plate armor remained in militaristic use for a lot longer than most people think. It wasn't really until armies became larger and state-supported that armored troops were abandoned for cheaper, more mobile troops.

The decline in practical usage of plate armor on the battlefield can be attributed to improvements in ranged weaponry. Starting with the English Longbow's ability to send arrows through the armor of Knights during the Hundred Year's War, these improvements would progress to firearms. Bowmen and riflemen became more practical than expensive knights. Only the thickest and heaviest plate armor could protect against projectiles, and as firearms became more effective, it became less practical to continue trying to improve plate armor.

However, plate armor would remain in use in varying degrees on the battlefield through the 18th century. Cavalry units used front and back plate armor for protection against long ranged fire, although infantrymen had long since abandoned the use of the armor in favor of cheaper attire.

Monarchs continued to wear elaborate suits of parade armor long after it became practical for protection, but they did not do so in a militaristic capacity (thus the term "parade armor").

As for swords, they are still in use in various militaries throughout the world today, although it is almost always in a strictly ceremonial capacity. For example, the United States Marine Corps allows Officers and Non Commissioned Officers to carry a ceremonial sword in some situations.

As late as WWI saw all infantry officers from all combatant nations carrying swords in the field. However, this practice lasted only weeks into the war, as they were impractical. British Cavalry mounted on horses carried swords up until the final switch to armored vehicles in 1938. Some officers carried swords into WWII, but they were outclassed by firearms.

In answer to your second question, swords remained in use long after armor fell into disuse. However, the decline of both happened largely in sync.

There's a serious western-way-of-war bias in your question in that you're clearly asking this in the context of two approximately equal military forces operating within the context of a war-time engagement clashing on a battlefield.

Broaden the definition of conflict somewhat and you'll find that swords continue to be an effective means of achieving political ends through violence even in the post-modern era.

I'm skating in under the 20 year boundary in mentioning this but between April and July of 1994 the Hutu Power movement killed something on the order of 500,000 to 1,000,000 Tutsis with machetes which are, after a fashion, swords (or possibly very large knives - I'm afraid the distinction is lost on me).

Now, obviously this is a case of a semi-military organization targeting civilians in the context of a genocide/civil war but while the wholesale eradication of a people falls outside of the acceptable bounds of war that does not mean that we can dismiss the weapon as ineffective or obsolete -- merely more niche in its application.

To that end I'd argue that the sword has become militarily obsolete within its context as a front-line battle weapon but within the context of its use as a weapon of terror, civilian persecution, and (especially) tribal conflict it remains relevant to this day, particularly in less affluent corners of the world.

This question deals with a similar subject: http://www.reddit.com/r/AskHistorians/comments/2sa1s2/gottfried_götz_von_berlichingen_a_famous_german/

Hopping in for a question :

Do we have any examples of a battle between clear-cut modern pike-and-shot and traditional knight-in-armor armies?