Quite often.  I'd say about 3/4 of the transactions.

Addendums either are used to sew up loose ends or contain a condition or subject-to clarity. I like using them to spell-out & emphasize the contract, deal points, additional work and to aid in maximum communications.

Almost every single deal.  If not during the offer itself, then during the repair request stage.  It's often far easier to reply with "See Addendum 1" on the form and list things out on the full page addendum.

Escrow almost always has at least one amendment too.  Usually around repair credits, changes in closing dates, etc.

I'm pretty sure I see more contracts that end up using addendums along the way than contracts that do not, either initially or through the process.  At closing, as long as all parties have kept up w/changes along the way, things should go seamlessly.  

Our contract is full of addenda & is 13 pages long. Check the particular paragraph that you need.

% would be 100% in my area that we use at least one.

The use of Addenda (plural of Addendum) is not unusual. We see them very often when an offer is submitted with several addenda including the removal of contingency addendum. Addenda, such as a contingency removal or addition of a signer to a contract which does not have enough signature lines or extension of time, can change the terms of a contract.

The contract is provided to the closing agent who is guided by the contract terms as amended.

I want to make the distinction here between an addendum and an amendment. 

An Addendum 'adds something' that needed to be added. 
An Amendment 'changes the original agreement'. 

They (here, AZ) may both use an 'Addendum Form' in our State forms to make those additions or changes.

My AIR forms have Amendment forms as well as Addenda. 

These days we use appraisal gap addendums on about every transaction.

Addendums are designed to be used in specific circumstances that apply to a transaction but not all transactions.

At closing, the customs of the particular state applies. Some use title companies and some use attorneys, while some allow closing agents.

Often, state dependent and property dependent.  Condos have lots of riders. 

  Frequently.

   Don't "write stuff into the contract"; don't line things out, or otherwise tamper with the boilerplate.    Use the addenda forms provided by your State or Local Association. 

Many are used all the time in both listings and purchases. 

Closings are managed differently from state to state - depending on who we represent as well as if attorneys are involved. 

More often than not - either part of the initial contract such as a VA/FHA addendum or to address changes and additions at a later time such as repairs, change in closing date, etc. 

I work mostly with listings and each one comes with a set of mandatory and optional addenda that goes with it.

I would say that most RPA's have an addendum attached to them.  The closing is different in many ways.  Here in California we use escrow for closing to no one is needed to be present.  Many states use Attorneys and meet at the closing table.

I average 3 per - deal every deal.

There one for my BRE there can be 1-3 for my RPA

And there's typically one for my RR-1.

As others have mentioned, commonly used to keep the contract clean.

As often as the need arises Mercedes! Everything is agreed upon prior to closing...recording is the end result.

Probably 50% of the time.