Because the cost to acquire a new customer is much higher than keeping an existing customer, and for many sites new visitors make up over half of all traffic -- offering incentives to new customers makes sense.
For example, Organize.com has used a pop-up coupon for first time visitors, offering $5 off if you buy something during your visit (not on your subsequent visit).
Here's another offer for first time visitors (I used a different browser):
Whether these pop-up incentives are a turn-on or a turn-off for your customers is something you'll have to test.
A few things to keep in mind if you explore this method of first-time-visitor personalization:
Should You Address "First Time Visitors" as Such?
Visitors that use different computers, browsers or who regularly clear cookies will show up as new visitors even if they've been to your site before. Same goes for visitors who visited some time ago whose cookies have expired. When these customers repeatedly see "Welcome first time visitor!" - what does that do to your brand? Does it become spammy?
And because offering discounts to first time visitors is technically price descrimination, it might put off some who think "What about us returning customers? Are we chopped liver?" You can still offer discounts without mentioning "first time visitor" as Organize.com does in the second example.
Incentives are No Substitute for A Clear Value Proposition
If you're going to use pop-ups, why not split test an incentive vs. a clear one-sentence explanation of why the customer should buy from you and nobody else? Give the first time visitor a compelling reason to stay -- especially when customers can easily find coupon codes in search engines for you or any of your competitors.
Don't forget, it's important that your UVP/USP (unique value proposition AKA unique selling proposition) is clear on your website for all visitors.
Deliver What You Promise
Test your coupons often to make sure the process works. The worst thing you can do is "forget" to apply or honor the coupon code at checkout. First time visitors are far less likely to ever return if they perceive they've been deceived.