I do not know abt govt organization.
As far as pvt org is considered, it depends on the employer/founder.
Few organizations (most being huge corporate) allow sick leaves to be carried forward up to a max limit of 'X' (a number decided by top mgmt)
I do not have any evidence for this but I know this as I was a HR summer intern there and was told of various benefits that the employees get there. Since we are not allowed to name organizations, i can just give you hint that it's a big corporate and is a dream company of many people in India.
Few organizations (and most of small and medium scale organizations) would lapse the leaves at the end of the year.
For my organization, we have drafted a policy whereby
Sick leaves lapse at the end of the year and can't be encashed
Casual Leaves (same as above)
Earned/Privileged Leaves - unavailed PL are encashed @Basic salary drawn at the end of the year.
Also we have introduced a policy whereby we give additional cash prize and recognition to the person who has availed least leaves in the year.
Hope it helped :)