A reader's comment made me realize I have not addressed the velocity question directly, so here is a chart of what is arguably the best measure of velocity, which is calculated by dividing nominal GDP by M2. The last datapoint uses my estimate of nominal GDP and M2 for the second quarter. I might be off by a little, but even considering a decent margin of error it is clear that the decline in velocity has really tapered off in recent months. Velocity fell by 7.6% last year, with the drop being the greatest in the fourth quarter: -5.6%. Velocity then fell 3.1% in the first quarter, and my guess is that it will fall only 0.5% in the current quarter.
The big drop in velocity is simply the result of consumers and businesses deciding to hang on to their money instead of spending it; a natural reaction to the sudden onset of the financial crisis which followed in the wake of the Lehman bankruptcy last September. The turnover of money (velocity) slowed dramatically as everyone sought to either increase their money holdings or pay down debt.
It's not unreasonable to assume that as the level of fear declines, people will resume spending their money. As everyone attempts to reduce their money balances, money will turn over faster, and nominal GDP will rise at a faster rate than money balances. Velocity, in other words, will rise. For the time being it looks more like velocity is stabilizing, but it will rise by the end of the year if the economy picks up speed.
One reason that M2 velocity is arguably the best measure is that it is the only velocity measure that has proven to be relatively stable over long periods. Note how today's velocity is back to the levels that prevailed from 1959-1989. Looks like one more thing that is "returning to normal."