Different Shapes

SS - put small graphic infront of the text, similar to (charts > chart types)

Rising - (or Positive) Yields are at "average levels" and the curve gently slopes upwards as maturity increases. Sometimes also referred as the Normal yield curve.
Flat -
Humped - Yields are high with the curve rising to a peak in the medium-term and then lower rates in the long-term.
Inverted - (or Negative) Yields are at historically high levels, with short-term rates substantially higher than long-term rates.

Rising

SS
Yields are at historically low levels with long rates significantly greater than short rates.
A normal yield curve slopes upward (asymptotically), the longer the maturity the higher the yield.
The market might be anticipating a rise in the risk-free interest rate. If investors hold off investing now they might receive a better rate in the future. Investors who are willing to lock their money in now need to be compensated for the anticipated rise in interest rate in the future.
A normal yield curve means that yields increase as maturity lengthens (ie a positive slope)
This reflects a growing economy with an expectation that inflation will increase.
The expectation of higher inflation leads to expectations that the central banks will raise short-term interest rates to slow down economic growth.
This causes uncertainty about the future rate of inflation and therefore investors want a higher yield as maturity lengthens.

On a normal rising chart - top line is forward rate, middle line is zero-coupon rate and bottom line is coupon bearing

Longer maturities entail greater risks for the investors.
This effect is referred to as Liquidity Spread.
If the market expects more volatility in the future, even if interest rates are anticipated to decline, the increase in the risk premium can influence the spread and therefore cause an increasing yield.

Yield-Curves move on a daily basis and tend to move in parallel with the movement in interest rates.

For example lets take US Treasury bonds and US dollar interest rates
Yield-Curves are usually upward sloping, the longer the maturity the higher the yield.

Flat

SS
This is when all maturities have similar yields
This indicates uncertainty in the economy.

Humped

SS
Where yields are high with the curve rising to a peak in the medium-term and then sloping downwards at longer maturities.

Inverted

SS
Decreasing Rate
Yields are very high by "historical" levels and long-term yields are significantly lower than short rates.
When there is persistent deflation, current cash flows are less valuable that future cash flows.
(ie a negative slope)
An inverted yield curve means that yields decrease as maturity lengthens.
Investors will settle for a lower yield now if they think the economy will decline further in the future.

For example in November 2004 the UK government bonds yield curve was partially inverted.
This occurs when the market anticipates falling interest rates.
Strongly inverted Yield-Curves have historically preceded economic depressions.