Well, according to the world media, including The Daily Mail and Gizmodo, a new method allowed the people to find 54 BCf (billions cubic feet) of helium in Tanzanian East African Rift Valley. The U.S. federal helium reserve (currently led by Janet Helium Yellen, assuming that algebra works) only has 24 BCf right now.
So Tanzania has more than twice the U.S. reserves. Since 2013, it was Qatar that was the main supplier of helium.
The new Tanzanian reserves are enough to fill 1.2 million medical MRI scanners. The recent global consumption was huge – 8 BCf a year (which eats the U.S. reserves in 3 years). In 5 years, the helium price went up six-fold.
The right-wing Daily Mail complains that helium isn't "renewable", something you expect from the greens. Paradoxically, it's the wife of a spinless extreme left-winger Sean Carroll, Jennifer Ouellette, who pointed out that helium is technically a renewable resource because it's being constantly created by the radioactive decay chains starting mostly with uranium.
Note that the Tanzanian finding is enough to fill some 100 billion large enough children's balloons – my estimate. Moreover, many additional findings of this sort may be made in the future. So I don't really believe that we should abandon the market rules for helium. I don't think we should ban helium balloon in amusement parks or YouTube videos incorporating funny voices modified by helium.
My answer from 2012:
Helium is relatively rare on Earth, 0.00052% of the atoms or molecules in the atmosphere (or the same fraction of the volume; much lower fraction of the mass). The concentration of helium in the atmosphere is low. Moreover, it's dropping because of atmospheric escape. About 4 tons of helium escape from the atmosphere every day because there's a significant probability that the helium atoms' speed exceeds the escape velocity, so there's no return anymore.
Because the amount of helium in the atmosphere is so low, that's not where we are getting it from. We are getting it from natural gas at places where it's created from alpha-decay of uranium and other elements – alpha-particles are helium nuclei. And such natural gas has up to 7% concentrations of helium so it's convenient to get it from there via fractional distillation. The depletion of helium from the "realistic sources" therefore occurs at a similar relative rate as the depletion of the "conventional" natural gas. If the helium escapes to the atmosphere, it's effectively lost. No one is going to catch the rare molecules from the atmosphere: you would have to grab huge volumes of the air to find the required amount of helium.
Different elements or compounds are being "depleted" or "accumulated" at very different rates. You must understand that for practical reasons, only the elements and/or compounds contained in materials where their relative concentration is high enough may be counted as accessible. So once they're lost, e.g. the helium in the atmosphere, they're lost and they can't be recycled.
The Earth's soil and crust and water contains some elements and/or compounds whose amount is effectively infinite relatively to the human consumption, so it makes no sense to talk about their depletion. The Earth will almost certainly be burned when the Sun goes red giant in 7.5 billion years before we would be able to deplete nitrogen from the atmosphere or silicon oxides from the rocks etc. The whole upper layers of the Earth are largely composed of such things.
We won't deplete carbon dioxide anytime soon; as long as we have any fossil fuels etc., the concentration of CO2 in the air will be kept elevated which is a good thing. However, it's true that a few centuries after we run of fossil fuels and similar things to be burned, CO2 in the atmosphere will converge back towards the equilibrium concentration dictated by the temperature (around 280 ppm for today's temperature). If this happened abruptly (it will take a century or more for the drop to occur), the plant growth rate would drop by about 20% and about 1 billion people in the world would have to starve to death rather quickly. Most plants stop growing below 150 ppm of CO2; during the coldest ice ages in the recent 1 million year, the concentration never went below 180 ppm or so and the plant species that wouldn't be able to survive this drop have gone extinct.
Some other elements or compounds are rare, e.g. gold and platinum. If you don't want to search for them 30 km beneath the surface (or try to bring them from other celestial bodies which is still prohibitively expensive – the price to get X kilograms of matter to the orbit is comparable to the price of X kilograms of gold and you would need even higher expenses to launch spaceships from Mars etc. to get the gold here), the total amount of these precious metals that can be "mined" isn't too much larger than what we have already gotten.
Concerning your "why helium question", let me just quote Wikipedia.
Multinuclear imaging: Hydrogen is the most frequently imaged nucleus in MRI because it is present in biological tissues in great abundance, and because its high gyromagnetic ratio gives a strong signal. However, any nucleus with a net nuclear spin could potentially be imaged with MRI. Such nuclei include helium-3, lithium-7, carbon-13, fluorine-19, oxygen-17, sodium-23, phosphorus-31 and xenon-129. 23Na and 31P are naturally abundant in the body, so can be imaged directly. Gaseous isotopes such as 3He or 129Xe must be hyperpolarized and then inhaled as their nuclear density is too low to yield a useful signal under normal conditions. 17O and 19F can be administered in sufficient quantities in liquid form (e.g. 17O-water) that hyperpolarization is not a necessity.(This paragraph is rubbish: helium is used for cooling and no replacement exists for this role. The alternative isotopes are other nuclei that may be observed instead of hydrogen.)
So the helium is the best one but it doesn't quite have a monopoly. Clearly, if we ran out of helium, it wouldn't be the end of MRI. But the price of the helium is finite, a particular number dictated by the balance between supply and demand, and it's simply still better for many users to use helium even though we will probably deplete it well before others. As the reserves decrease, the price will increase and the proportion of other isotopes used in MRI will go up.
June 28th is the St Vitus day. The Prague Castle's main cathedral is named after him. Up to today, I didn't know he was a Christian martyr, a boy who died when he was 12 years old. It's not bad for such a boy to inspire such a cathedral.