AdWords Remarketing for search allows you to change your bid for a keyword if the user has been to your site before. Here are some interesting tactics to utilize this new feature:

Drive Incremental Sales With High ROI
Its hard competing with broad keywords while maintaining your ROI goal, as a result these broad keywords tend to be left inactive. So, create an adgroup that only competes in auctions for broad high volume keywords if the user has been to your site before.
Implementation:

1. Create an adgroup for your high volume keywords
2. Create a remarketing list for visitors to your website
3. Add that remarketing list containing visitors to your adgroup

Bid More For Repeat Customers
If you have data that shows repeat customers on your site have an average basket size that is 20% larger than that of a new visitor you can bid more aggressively to put your ad in front of those repeat customers.
Implementation:

1. Create a remarketing list based on visitors to a purchase confirmation page
2. Add that list to a copy of an existing Adwords adgroup
3. Edit bids so that they increase bids by 20% (or whatever) versus your original adgroup

Stop Paying For Clicks From People Already Subscribed To Your Email
If you have a goal to convert users to your email marketing list then you would want to exclude current subscribers from ever seeing ads. Once they have visited a page on your site that only email subscribers can get to, you can exclude them from your search campaigns.
Implementation:

1. Create a remarketing list based on visitors to a subscription confirmation page.
2. Navigate in Adwords to an existing campaign aimed at obtaining new subscribers
3. Add your remarketing list containing visitors to your subscription confirmation page
4. Click Custom Combinations
5. Choose None of these audiences (“NOT” relationship)

Treat Different Users Differently
If your website has three different offerings to visitors you may want to message those repeat visitors with tailored ad messages.  So, customize the advertising message these visitor groups will see.
Implementation:

1. Create three remarketing lists by putting three different remarketing tags on different portions of your website
2. Make three copies of an adgroup
3. Edit adtexts for each adgroup copy to put the most appropriate message to the users
4. Add the appropriate remarketing list to each adgroup

Re-engage Comparison Shoppers
If your customers tend to compare you to your competitors back to back you could serve ads on competitor’s brand terms only after they have visited your site first. Bidding on competitor’s brand terms tends to be expensive but using remarketing for search could make it more affordable.
Implementation:

1. Create an adgroup for your competitors keywords
2. Create a remarketing list for visitors to your website
3. Add that remarketing list containing visitors to your adgroup