Ancient Ruins in Civilization V are remnants of extinct civilizations, mementos of past greatness and order amid the chaos of the wilderness. Budding 'contemporary' civilizations may learn a lot from these places, which will help them in their first steps.
When landed on by any unit, Ancient ruins give a reward to the owner of the unit. This is a one-time bonus, after which the ruin disappears. These rewards include:
- A crudely drawn map of the surroundings of the ruins (Reveals some of the nearby tiles; note that the center of the revealed space is not the Ruins tile, but somewhere 3 - 4-tiles away in a random direction)
- Evidence of Barbarian activity (Reveals location of one or more nearby Barbarian camps)
- Secrets of the ancients (A random ancient era technology. Note that all pre-requisites for the technologies have to be met, so you can't get one of the more advanced techs (on the right-hand side of the Ancient Era tree) until you've discovered its pre-requisite)
- Survivors, which join your civilization (+1
Population Population to a city of yours) - Advanced weaponry (An upgrade to the unit you used to activate the ruins):
- Gold treasure (approximately 50 - 100
Gold Gold) - Cultural artifacts (approximately 10 - 20 Culture Culture, usually 20)
- Religious artifacts (30 Faith Faith)
- A prophecy (80 Faith Faith; only available after the player has founded a Pantheon)
And only at the easier difficulties :
The choice of reward is random in most cases, but it seems that sometimes some ruins are bound to a particular benefit, for example unit upgrade, and will always bestow it upon activation. Also, some benefits can only be activated after you've received another Ruin benefit (for example the Prophecy benefit you can get only AFTER getting the Religious artifacts from another Ruin).
Finally, it seems that not ALL Ruins have the full range of possible rewards, with some of them having a pretty limited choice of the less-powerful ones. This is best seen when using the Pathfinder's ability which gives you a direct access to each particular Ruin's list of rewards.
Brave New World
Thanks to the new Archaeological system, in Brave New World ancient ruins will later spawn Archaeological sites! So, try to remember the locations where you've encountered and activated Ruins, so that your Archaeologists may return there later to dig and uncover more valuable secrets!
Strategy
An ancient ruin ingame
The discovery of Ancient Ruins is vital for the early development of your civilization. The bonuses might seem small, but for the very beginning of the game they are very significant. A single citizen may considerably speed up the development of your capital. The 
Culture Culture bonus may instantly give you a Social Policy (or speed up acquiring the next one). The 
Faith Faith bonus may allow you to start a Pantheon even though you haven't constructed any Faith-generating building. Also, upgrading Scouts gives you Archers, even at a time you possibly can't afford to build these yet, while upgrading Warriors gives you the more powerful Spearmen, allowing you to fight Barbarians more effectively. And, of course, a free technology is always welcome!
In Brave New World, the Shoshone civilization's unique unit, the Pathfinder, may choose which of the rewards to activate upon entering the Ruins. Needless to say, this allows him to choose at will the path of his development.
All in all, the discovery and activation of Ruins might give your civilization a crucial advantage in the early game. It should become an integral part of your early game exploration, and it's highly recommended, regardless of which civilization you're playing as, to consider building a Scout first upon settling the Capital, and use it along with the initial Warrior unit to explore as far as possible.
Historical Info
Ancient Ruins are the remains of earlier long-dead civilizations. They are filled with valuable secrets - gold, maps, lost technologies and sometimes even survivors - awaiting discovery by the intrepid explorer. Rich rewards await those who first enter an Ancient Ruin!