I'm contributing the max to my HSA for 2010 ($6150/year for family plan) via twice-a-month payroll contributions. However, my HSA balance can't keep up with incoming medical bills, and I'm having to pay some of them from other non-HSA accounts. I understand I can reimburse myself from my HSA once the balance is sufficient. If I'm not able to reimburse everything this year, can I continue to pay myself back from the HSA next year for medical expenses incurred this year?

As long as you have the HSA account active and a qualified health plan in force at the time that the expenses were incurred. Yes.
The only accounting you would need to make is at an IRS audit. As long as expenses are greater than withdrawals.

As long as you have the HSA account active and a qualified health plan in force at the time that the expenses were incurred. Yes.
The only accounting you would need to make is at an IRS audit. As long as expenses are greater than withdrawals.