Certainly, the Euro's (FXE) weakness versus the dollar hasn't gone unnoticed. In just the last year, the EUR/USD cross (ERO) has gone from 1.45 to 1.21, a 16.5% drop. This weakness comes essentially from the uncertainty regarding the Euro's future. Fears of a breakup exist, as much as there are fears that some of the periphery countries, such as Greece or Portugal, might be forced to leave the common currency. Or might opt out of it.
These fears are not unfounded. It would perhaps be easier for some countries to opt out of the Euro, get their currencies back, dilute and devalue their currencies and be done with the structural corrections they need to undertake. This path is somewhat easier than the internal devaluation path that's being taken, which forces governments to cut nominal wages, leads to higher unemployment and a lot of grief. Granted, these countries wouldn't be much better if they went through the devaluation route. But it would seem better and easier.
Yet, all these fears and uncertainties that are tightly coupled with the austerity programs hitting most of the periphery countries, have another angle to them: Basically, that which ails the Euro also makes it stronger. By implementing austerity programs that seek to bring equilibrium to these countries external imbalances, the imbalances are really being corrected (as can be seen by the collapsing current account deficits in Portugal and Greece). Compare this to the U.S., where no such efforts are ongoing, and as such both the budget deficit and the external imbalances remain about the same.
Ultimately, correcting the external imbalances in the weaker European economies lowers the likelihood of the need to print money down the road. And not doing it in the U.S., increases the likelihood of needing to print more money down the road. And this is what, longer term, means that today's measures and fears will make for a stronger Euro tomorrow. If Europe stays on this road, at some point it will have produced a healthy economy, whereas the U.S. will still have the same rotten QE-needy quagmire it has today. Such will make for a weaker dollar, and a stronger Euro.