What's In the Case?

This is deliberately ambiguous, and unknowable.

It's a classic Macguffin; something that is purposefully not disclosed to heighten intrigue.
The film's IMDB FAQ page lists a number of speculations, but out-of-universe the directors have intentionally kept it incalculable.

The briefcase is a "MacGuffin" - a term popularized by director Alfred Hitchcock and writer Angus MacPhail to describe a plot point that is deliberately left vague so as not to draw too much emphasis away from the real story. What is known about the contents is: (1) It is worth more than $800,000 (the maximum the Irish are willing to pay the mercenaries since they cannot afford to bid for it, and about the same amount that can fit in Gregor's briefcase at the end of the film); (2) It is wanted by both the Russians AND the Irish, but neither is willing to pay for it; (3) It is small enough to fit inside an ice-skate case, and not too heavy to be handled by a variety of characters; and (4) It cannot be hazardous material, since Gregor was able to mail it to himself through the French postal system, who would check. Some speculations are: (1) Important or stolen blueprints; (2) Printing plates for the new (at the time) Euro bills; (3) Important or stolen documents. and (4) The ice skate case belongs to the Russians and contains information that they want back. (Details of arms sales? Pictures of Mikhi with underage boys?).That's why Mikhi wants it back but doesn't want to pay for it; handing over money could validate the contents and be used to blackmail him later. The Irish want it as leverage over the Russians. The CIA want it to convict the Russians. The man with the case wants to sell it and make a quick buck.

So I'll start with the obligatory "it's a MacGuffin" yada yada yada. Obviously the audience is never meant to know and it's probable that the director and writers never gave the item a concrete reality; that is to say, there probably isn't any "correct" answer. That said, as long as we assume that the events of the film and the way people acted are meant to be consistent with whatever "it" actually is, we can rule out quite a few things.

The biggest clue is that while people are willing to bid or spend high amounts, none of the players seem willing to actually complete a transaction of cash for the item. The IRA (or at least Seamus) are willing to pay contractors hundreds of thousands to steal the item but not to bid on it. Similarly, the Russian Mikhi repeatedly pretends to be willing to pay for the item but never actually is. A potentially important clue is that in both cases while the interested parties are referred to as "the Irish" or "the Russians", it seems to actually be individuals that are interested in the item, not the larger groups. For this reason, plus the fact that we don't see other groups interested, not even the CIA who view the contents of the case as completely secondary to the goal of capturing Seamus, it seems fair to rule out any object with intrinsic value. So it's not jewels or money printing plates or even a weapon of some kind, because all of those things have an intrinsic value that would both attract other bidders and would not cause people to balk at paying money for it. This would also seem to rule out state secrets like like the identity of secret agents or blueprints to the US embassy or whatever, since the CIA and other nation state actors would definitely consider those important.

So what's left? The identities of the interested parties and the events at the end of the film suggest that the item is evidence of some kind. Evidence that specifically involves the interests of Seamus and Mikhi. My guess is that it's evidence of some past interaction between these two players. Each man wants the evidence to prevent it from being used against him at some future point but doesn't want to directly purchase the item because that in itself could be considered verification that whatever the evidence is, it is both real and accurate. The fact that the men aren't working with each other could suggest that each of them could use the evidence in some fashion against the other. Perhaps Mikhi could use the evidence to blackmail Seamus by showing that he was working with people that would anger the IRA leadership or that Mikhi was working angles not sanctioned by the Russian government. This is indirectly supported by the radio broadcast in the last scene of the film which announces that the IRA are ceasing hostilities and negotiating with the British government. The death of a single individual wouldn't seem like reason enough for the IRA to end hostilities, but perhaps the recovery by the CIA of the item allowed them to inform the IRA leadership that they had been mislead or that some play by Seamus had been dismantled, either freeing them or forcing their hand in the matter.

Of course this is all pure speculation, but information is the only thing I could think of at the cross section of 1. no intrinsic value 2. a very specific set of interested parties and 3. no one wants to be seen as taking ownership of the item in a traceable way. We'll never know for sure, but for me this is enough of an idea of what it might have been to quench my thirst for further answers.

Could it be English pound conterfeit plates, something that the IRA could use against England as Hitler did. Something that the Russians could also use against them and that the CIA would wish to aquire before that happens thus preseving the World economic stability.

Based on the prices being offered, and the willingness to kill, and the fact that Shamus is a terrorist (revealed at the end of the film's news story), there is a strong possibility that it was a nuke of some kind, as they could have gotten explosives from anywhere. Had it been mentioned in the film that it was in fact a nuke-then it really would have changed the whole story at least in part. I like that they kept it vague, more like an unknown prize.

Probably vital intelligence about CIA undercover operatives in Europe? Why would the IRA want it so badly?
There is also GPS satellite navigation equipment for ships which fit in the suitcase and are not too heavy to handle.
I can imagine both IRA and Russians like to stir some shit up with sending a ship off course.
Or a vital peace of intelligence containing the identity of undercover CIA operatives.
Any of these would explain why Sam as an American is on the team.
But I think the entire point of the movie is to put us in a position where we, like the characters, are desperate to know what's in there. Like them, however, we will never find out. "NO questions and NO answers. That's the business we're in. Accept it and move on" is the final lines of movie.

Some higher grade of Uranium, 235 would be by bet. It also could possibly be Plutonium.