What is currently the cheapest way to get USD from a US bank account or cash to an exchange like btc-e?
Dwolla is among the cheapest methods of moving funds from your bank account to an exchange. The exchanges which accept Dwolla are Mt. Gox and Camp BX. The cost is just $0.25 per transaction. The drawback is that there is a 30-day probation period after your first funds are pulled into Dwolla before you can then transfer money to a Bitcoin exchange.
Another method is Coinbase. They charge 1% and their exchange rate is close to Mt. Gox. The problem is that they max out at $100 per transaction.
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http://www.CoinBase.comFor larger amounts, Bitcoins Direct, a "bulk" dealer, is inexpensive. They have a minimum $1,000 per transaction limit though. They also don't always have coins for sale.
BitMe allows cash deposit at a Chase bank location. The problem is that the liquidity isn't always that great, and slippage can occur -- sometimes even for a few hundred dollar's worth.
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http://www.BitMe.comIf you have or can get ING direct, then that method to BitFloor might work. There is a history though following their security breach that you may wish to familiarize yourself with though before choosing this option.
So that leaves bank wire to an exchange (such as Mt. Gox). Bank wires are a costly method for anything but larger transfers.
Now there may be somone local who is trying to sell. Sometimes they are just looking to trade at the current exchange rate (no fees).
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http://www.LocalBitcoins.com