Time until All Glaciers and Ice Caps Melt at current rate: ~ 38,000 years

James Hansen of NASA/GISS says his grandchildren could inherit an ice-free earth, and that a warming ice-free earth would cause a sea level rise of 75m. According to recent estimates, about half (~1.6 mm/yr) of recent sea level rise is due to melting of ice sheets and glaciers, and the other ~half due to thermal expansion (both of which have been happening since the last major ice age). Assume also: 

1. Total volume of water on Earth: 1,260,000,000,000,000,000 m³

2. Total volume of water bound in icecaps and glaciers: 1.6% = 20,160,000,000,000,000 m³

3. Total volume of water in the oceans: 98% = 1,234,800,000,000,000,000 m³

4. Assume sea levels continue to rise at the same rate of 3.2 mm/yr by satellite altimetry (even though data indicates this is exaggerated and the rate is decelerating)

If all the ice in icecaps and glaciers melted, the total volume of water in the oceans would then be 1,254,960,000,000,000,000 m³, an increase of 1.6% from the present. Since the average depth of the oceans is 3790m, a 1.6% increase in volume would cause a sea level rise of 3790*.016 =  60.64m = 60640 mm. At the current rate of sea level rise over the past 18 years by satellite altimetry (a decelerating 3.2 mm/yr), half due to ice melt is 1.6 mm/year,  thus it will only take 60640/1.6 = 37900 years until all the ice in glaciers and icecaps melt at the current rate. Add to the fact that the Greenland and Antarctica ice sheets are currently increasing in volume and we are overdue for another ice age, the time is further postponed if ever. Not to mention, fossil fuels will run out within 200 years or less. 

The sea level has risen approximately 120m since the peak of the last major ice age approximately 20,000 years ago. Although the rate of sea level rise has greatly decelerated over the past 6000 years, the rate over the entire 20000 year period is 6mm/year. Substituting .5*6 = 3 mm for 1.6 above yields 20213  years until all ice is melted. Note: melting sea ice causes no significant change in sea level due to Archimedes principle.