You may achieve it using Extra Objects (Curve) add on, then beveling a curve and edit it with a proportional editing.
Activate the add on in User Preferences (Ctrl+Alt+U).
Go to Add-->Curve-->Spirals.
Play with a spiral's settings in a Tool Shelf (T).
When you're done keep extruding the bottom segments of a curve to create vertical part of a corkscrew. Add a Bezier Circle and use it for beveling the curve.
Finally enable the proportional editing, select the very end segment of a spiral, then press Alt+S to adjust its bevel radius. Use Mouse Wheel to adjust the influence of proportional editing. To make the end of the spiral sharp select the last curve's segment and press Alt+S, 0.