A lot of the dollar strength has to do with two things:
1) The dollar is the reserve currency of the world, making it the denominator of most commodity exchange (i.e. oil) and international debts (including anything loaned by the IMF or World Bank). As other economies go sour, governments, companies, and private investors buy up dollars with other currencies so that they have their holdings in the reserve currency so they can buy goods, invest, pay back debt, etc. This increases both the demand for the dollar and the supply of other currencies, doubling the effect of the shift/spread in relative values.
2) As investors lose money in stocks they shift to Treasury bonds, which are very safe and pay a little interest to boot (not enough to beat inflation, but at least you don't lose numerical dollar amounts). Bonds are effectively a contract on debt, subsidizing the US gov's printing and spending. The purchase of bonds, therefore, floats that debt, staving off inflation, and keeps the dollar at a higher value. Again, add this effect to the relative drop in value of other currencies discussed above and you see why the dollar is doing so well.
I'm no economist, and there are a lot of people here who can correct my points and give you a much more detailed explanation, but those two factors certainly play a large part.
As for gold, that one yesterday had me baffled as well. Back at the bailout time gold jumped as the market went south as one would expect, but now it seems to be falling. I think it has to do with a panicky shift to bonds yesterday as the market dropped, and I would expect it to edge back up slightly in the coming days and then go up a little more near the end of the month in anticipation of the futures contracts coming due. As for the decline since March, it probably has a lot to do with the overall health of the economy - back in March everybody was still playing hard and driving up precious metals like everything else, but things have changed and people don't have the expendable playtime investment money they had then and have shifted to safer investments (in terms of volatility, not real value).
The thing to remember about the dollar, though, is that it is at the mercy of investment. If, say, the Chinese dumped their reserves to pay for their stimulus package or OPEC decided it was time to accept only Euros as payment, we'd be screwed as inflation ate away at the purchasing power of every dollar in our pockets. Remember, the dollar has lost 25% of its purchasing value since 2000 - inflation is alive and well; this situation would get much worse if the world decides the US economy isn't strong enough for the dollar to remain the reserve currency.
If you have money that doesn't need to be immediately liquid, I would buy a little gold and a lot of silver right now, no matter what the prices do in the short run. In the long run they are profitable investments which have intrinsic value (something that can't be said for stocks or dollar-denominated savings).
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