If I renew my passport do I get 10 years from the expiration date or 10 years from the renewal date?

It depends on what country issued your passport

If you have a British Passport, and renew it early, then Time left on your existing passport will be added to your new one - up to a maximum of 9 months. Thus you can have a British passport with an expiry date 10 years and 9 months into the future.

However, many countries don't extend the validity of a new passport based on time left on the old one, so you won't get any credit for renewing early. Australia is one such country, there are many more.

Generally, if you look up the rules on passport renewal and you see something about transferring time from an older passport then it'll be done. If you don't see anything about it there, then most likely your country doesn't offer it.

Logically, it will be from the renewal (issue) date. Otherwise the passport will be valid for more than 10 (or 5 years depending on your country, some countries like Jordan issue a 2 years passport sometimes).

Lets say you renew your passport in December 2012, if the expiration date will be 10 years from the previous passport's expiration date (December 2013 in your case) then the new passport will have the issue date of December 2012 and expiration date of December 2023! Your passport which will have a new passport number will be valid for 11 years which is logically wrong.

Anyway, Some countries, Like Sudan and Egypt, before they start issuing the new passports with the bar code, they used to add a renewal stamp which will usually has a new date of expiration which will be n years added to the previous expiration date. These were the good days when passports used to be hand written and this is not valid with the new passports.

UPDATE: It seems that UK citizens can have passports for more than 10 years (check the comment by Gagravarr). I think this is an exception.

For USA passports, the new passport is valid for 10 years from the issue date. See "How long is a passport valid and when should I renew my passport?" in the passport FAQs.

My boyfriend had to get his passport replaced (for name issues) recently, and even though his previous passport was only a year old, his new passport is still valid for the 10 years.

In the case of Italy, the passport is not renewed but re-issued. Quoting from the Italian Police website:

Il passaporto è rilasciato ai cittadini italiani e ha durata decennale. Alla scadenza della validità, riportata all'interno del documento, non si rinnova ma si deve richiedere l'emissione di un nuovo passaporto.

With this in mind you can easily guess that you will get a new document with 10-years validity starting from 00:00 on the day of renewal to 23:59 of the day before that of renewal plus 10 years.