I just read in my other post that a person just started to play this game, keep this in mind when I say this. People have made a suggestion that we end the war with the klingons, and some have said that we should remove it all together. Now if someone just starts playing the game, they will miss out on that content.
The Federation is not at war with everybody. Everybody's addressing the other points made and ignoring this one, but this is a bit of a peeve of mine.
Progression of events in a persistent world is weird, since new players go through those events and not always in the same order as older players (especially with Cryptic's way of imbedding new mission inside of existing progression). However, the general rule is old content has already happened, new content is happening. By those rules, current Federation relations:
Klingons and allies: Leadership officially claims a state of war but actual fighting has been limited since B'vat's death. Fleets have operated in multiple theaters without conflict and have had a true joint operation in one.
Romulans: Partially resolved. Both large fleet buildups on their part were defeated, and the only splinter factions with currently stable leadership are not enemies . Conflict with one of the other factions continues on and around New Romulus, but has not yet escalated as it did previously. (Anniversary event could progress this).
Cardassians: Resolved with the defeat of the True Way Leader.
Dominion proper: Aside from a skirmish in the wormhole that didn't escalate, there has not been conflict with the Dominion. They did not support or join the time displaced fleet, and even aided in its removal (granted not on friendly terms, but not hostile ones either).
New Link: No contact since Laas was defeated, last communication was a mutual agreement to leave one anther alone.
Terran Empire: Incursion was ended. War may arguably be still in effect, but the gate was closed.
Breen: Resolved at Lae'nas III. Only thing the Breen are doing now is collecting slaves, which they've always done.
Borg: The Queen has been destroyed, not to mention the wholesale destruction of Borg hardware on an epic scale. Forces are still present and still hostile, but canon implies the destruction of a Queen causes at least temporary disarray. This war is partially resolved, though probably not forever.
Undine: It's unclear how much infiltration remains, but open conflict ended when the Undine destroyed the SS Seleya. We retreated from fluidic space at that point and have not returned. Future contact and conflict will probably be unavoidable, but has not happened yet.
Tholians: An interesting question. Battles with them so far has been by intervening in conflicts between them and third parties, not a direct war with them. Their intentions are still pretty much unknown.
Iconians: Not at war yet. Of the encounters with Iconian ships, only one actually attacked and did not do significant damage (which in other encounters they proved they were more than capable of).