HSA Improvement and Expansion Act of 2006 - Amends Internal Revenue Code provisions relating to health savings accounts (HSAs) to: (1) allow a one-time, tax-free transfer of balances in employer flexible spending arrangements, health reimbursement arrangements, and individual retirement accounts to HSAs; (2) revise HSA eligibility criteria for spouses covered by flexible spending arrangements, individuals over age 65 automatically enrolled in Medicare part A, and veterans receiving medical benefits; (3) increase contribution limits for HSAs; (4) allow payment of high deductible health insurance premiums from HSAs; and (5) allow payment from an HSA of certain medical expenses incurred before the establishment of such HSA.