What if Boudica won the Battle of Watling Street?
Nero would send another general (probably Corbulo) back and utterly beat the living snot out of the Iceni. Alternatively, the Romani just abandon the hellhole that is Britannia, don't have to spend extra money on its defense, and probably do better during the Crisis of the Third Century. Plus, since Britannia was always a breeding ground for usurpers, they don't have to deal with as many civil wars, either. Bonuses all around for our favorite genocidal world-conquering Italians.
Vandal Warlord said:
What if The Romans invaded Ireland?
They would withdraw a la Germania because fighting insane Goidilic warriors over a crappy and unprofitable piece of land is stupid.
Vandal Warlord said:
What if Ireland invaded England (Middle Ages, not now) ?
You mean, like Brian Boru Ireland or the Ireland during every other point in the Middle Ages?

It didn't really have the resources or the centralization or even the motivation to attack. Besides, usually the Irish were fighting off invaders in the Middle Ages, with a brief window between the Norwegians and the Norman English when they fought each other more ferociously. So there's really not much of a reason to get them to invade other places when they're being invaded themselves right then.
Interesting question: as improbable as it is, a British Revolution during the 1770s was still possible. Social tensions were starting to burst the country at the seams, and the government wasn't all that competently run either. Besides, in many cases the French Revolution wasn't all that plausible either. What if it happened in Britain instead of France: what if George III and Parliament went to the knives with each other and ended up fighting another Civil War?
(No, this idea is not particularly original, as
some may point out. It is, however, all I could come up with in ten seconds.

)