Break Out Your Magic 8-Ball

I have no idea as no one can know for sure. If I had to guess, it would probably be ancient/medieval Indian/Arabic coins. They are a relatively quiet series, meaning prices are comparatively low, and fakes are not as rampant as in other series. As more people get discouraged by high prices in the more-popular coin series, I feel that they will enter these ingored markets and eventually drive up demand and prices.

I like the gold Liberty Head quarter eagle. Many coins in the series are relatively inexpensive when compared to the mintage and rarity. The liberty head quarter eagle seems to be a overlooked series when compared to the popularity of the gold Indian Head quarter eagle.

Next big craze: I would say what started the last big craze? State Quarters. So the next big craze will be something similar. Either the quarter goes back to pre1999 design (or some other static design) causing all these multi year design changes to become more sought after, or the DIME has a design change to create this type of excitement. In any event, the craze will be driven by new entrants into the coin collecting field in my opinion not the excitement of collectors in the hobby right now.

Surge in value: Ike's are a good answer due to being a short run and being last big dollar. However, unless you have high grades I do not think you will see much of a surge.
High grade Mercury (>= 1934) dimes are low cost (undervalued in a lot of years I think) and a solid option for a surge. And they are recent enough that people (the individual, parents, grand parents) can still remember using them so they have a bit of connection.

The next big craze might be Swedish Kronor coins. Here's why:

In the months before The Netherlands converted to the Euro, a lot of people apparently thought it was a good idea to use all the spare change they could find before it got demonetized. As such, I picked up quite a stack of silver 1 gulden and 2,5 gulden coins from circulation, even though they hadn't been minted with silver for about 40 years.

Now that Sweden stopped producing their 25 mm 1 Krone coin, we might just see a lot of people doing the same, blissfully unaware of what they actually are holding: Swedish one Krone coins with silver content are still valid for payment until July 2017. There might just be a run on Swedish kronor coins from circulation.

Anything silver.

A friend of mine has a small hoard of older European coins from her grandmother. Can you aim me at a good resource to help her get a notion of their value?

First of all, after extensive research in the field, I found that the worth of a coin significantly depends on where you buy or sell it. the closer to 'home' a coin is, the more expensive it usually gets, if you're having coins from a country with a coin collecting community.

Having said that, the best I can advise you is to take pictures of it and post them here in the world coin forum. A lot of country-specific coin collector fora are in local language, so a more or less international coin forum as this may be a good shot.

Thanks! I've already invited her over to let me go through her US coins and give her a ballpark. She is busy enough that'll happen after the 2nd Coming. But if she does, I'll get pix!