Healthcare Cost and Utilization Project (HCUP) data from 2010 provide the most comprehensive national estimates of 30-day readmission rates for specific procedures and diagnoses.* Examples include (picture of a revolving door dividing halves of the image - one half is labeled By Procedure, the other By Diagnosis):

By Procedure (Picture of five people, with one person following an arrow into the revolving door) 
 Nearly one in five patients with these common procedures was readmitted:
  23% Amputation of lower extremity, 19% Heart valve procedures, 19% Debridement of a wound, infection, or burn.

By Diagnosis (Picture of four people, with one person following an arrow into the revolving door) 
 Nearly one in four patients with these common diagnoses was readmitted: 
  25% Congestive heart failure, 22% Schizophrenia, 22% Acute and unspecified renal failure

Nearly one in three patients with these less frequent procedures was readmitted (Picture of a person with the brain, an arm wound, a heart, and kidneys visible):
  29% Kidney transplant
  29% Ileostomy and other enterostomy
Nearly one in three patients with these less frequent diagnoses was readmitted:
  32% Sickle cell anemia
  32% Gangrene

Readmission Rates by Payer (flanked by icons of an IV and a clip board)
Medicaid and Medicare patients have a higher percentage of readmissions than other payers 

Procedure: Amputation of lower extremity (Bar chart of payer percentages) 
  Medicare: 26%, Medicaid: 22%, Privately Insured: 17%, Uninsured: 13%
Diagnosis: Congestive heart failure (Bar chart of payer percentages) 
  Medicare: 30%, Medicaid: 25%, Privately Insured: 20%, Uninsured: 17%
*Readmissions were for all causes and did not necessarily include the same procedure or diagnosis as the original admission (index stay). 

Source: HCUP Statistical Briefs #153 and #154: http://www.hcupus.ahrq.gov/reports/statbriefs/statbriefs.jsp 
(logos of HCUP, Department of Health and Human Services and Agency for Healthcare Research and Quality)