I used the top 3 (posted) dilemma piles of every regional with 8 or more people, the top 2 of every regional with 6-7 people, and the winning dilemma pile of every regional that had 5 or fewer attendees, for a total of 67 dilemma piles reviewed. I tallied both the total number of appearances of each dilemma in those piles, as well as the number of decks each dilemma appeared in.
The following charts express the percentage of those 67 piles that include each dilemma that appeared at least once. While it may be interesting to note that there were 97 Hard Times in those 67 piles (as opposed to "only" 71 An Issue of Trusts), I figured it would be more important to know how frequently you're likely to see a pile that includes specific dilemmas.
An Issue of Trust is still the king. Despite Klag, Neral, The Central Command and others, An Issue of Trust is still one of the best bets out there. It needs some targeted personnel removal and/or interrupt prevention, but it is still a great card against not only the most powerful affiliations out there (except Borg), but also every other affiliation (except non-AU Starfleet). Expect to see this card, and expect to not be able to do much about it. In fact, expect to see "randomly select all but one to be stopped" a lot, as Personal Duty and Picking Up the Pieces are also quite popular.
People love dilemmas that don't go under. Hard Time, Polywater Intoxication, and The Dal'Rok have always been popular, Occupational Hazards has been slowly gaining momentum, and Healing Hand and Honorable Pursuit have kept most of their early popularity since their introduction last year. There's no Occupational Hazards equivalent for Treachery decks, so Honor-free is more popular than ever - so it's no surprise that HP's popularity has slipped relative to HH. Medical-free is also something that pops up in decks now, so that has boosted the popularity of cards like Left Behind and Mugato. Infinite Diversity is nice for that same reason, since you can adjust on the fly what skill you're punishing the opponent for leaving home without.
Targeted personnel removal is everywhere. Secret Identity may "only" be the #3 card, but that's in part because many decks don't use both it AND The Caretaker's "Guests". Other popular options include He Wasn't Nice and Inequitable Exchange, though Johannes alone is responsible for at least half of the dilemma piles that include the latter.
Cost-punishing dilemmas are still around. Coolant Leak and In Development are enjoying roughly the same popularity, and Pitching In has hit the top 5. Miner Revolt has taken a hit from the likes of Archer and Assess Contamination, but it is still around as well. I estimate that the more popular these cards are, the better off the Klingons will be.
Tragic Turn has appeared in only one top deck since it was nerfed. While it is still far from worthless, it is no longer the powerhouse it once was. Unfair Comparison decks have emerged to fill its void; they didn't appear much until the second half of the regionals season, and from there I saw a fair number of them.
Wall dilemmas tend to be Planet or Space. Dignitaries and Witnesses notwithstanding, wall dilemmas tend not to be dual. Rogue Borg Ambush and Gomtuu Shock Wave are everywhere, and Where No One Has Gone Before isn't far behind. Even though RBA is by far the most common planet wall, planet walls have far more diversity than space walls.
Planet-first remains a bad idea. In part due to the appearance of Unfair Comparison piles, Necessary Execution has appeared frequently, as well as Distress Call. These cards do not appear only in UC decks though, so throw UC with caution.
Anti-megateam dilemmas are relatively uncommon. Getting hit hard by a Fractured Time (the most common one) can be devastating though, so it still may not be worth the risk. Bio-neural Computer Core shows up in a lot of Borg decks, and Restricted Area is in many Cardassian decks, so megateam with extra caution against those affiliations as well.
Cheap dilemmas that stop (or kill if you cannot) are common. Triage shows up a lot to punish people for not bringing medical, and Guess Who's Coming to Dinner? is popular for its natural combo with the most popular space dilemma. Back Room Dealings is also common; that one guy with double treachery may not be enough to protect you against Occupational Hazards. GWCTD? and BRD both give Locutus ten points, but their advantages seem to outweigh that disadvantage. This dilemma category looks to be extra important with the recent rise of the Romulan stooges + Karina at the NA and European continentals.
Dilemmas with event-based cost reduction are very common. They appear in multiples in the vast majority of Unfair Comparison piles, but the main advantage that a UC pile has over a straight Overwhelmed pile is they tend to remain functional even when the events are nuked with a Desperate Sacrifice or Quinn. The 7/8-costers also tend to show up 1-2 at a time in any deck with plenty of events, so be prepared.