Googlemaps, Bing Maps, Yahoo Maps and the USPS API are free. Why would I use LiveAddress for address verification?

There are actually more free services than that. I'll list a few that I know of:

Fedex, UPS, USPS, GoogleMaps, Mapquest, Bing Maps, and Yahoo Maps (are they still around?).

They each provide a certain aspect of their addressing services for free for the benefit of their customers but they also have terms in their agreements that govern how you can use the service. If you are breaching these terms (even if you are unaware of them) you expose yourself and your business to possible legal actions.

Here are the links to the Terms of Service for a few of them:

GoogleMaps

No Mass Downloads or Bulk Feeds of Content. You must not use the Service in a manner that gives you or any other person access to mass downloads or bulk feeds of any Content, including but not limited to numerical latitude or longitude coordinates, imagery, visible map data, or places data (including business listings). For example, you are not permitted to offer a batch geocoding service that uses Content contained in the Maps API(s). [10.1.3c 27Jan2012]

No Use of Content without a Google Map. You must not use or display the Content without a corresponding Google map, unless you are explicitly permitted to do so in the Maps APIs Documentation, or through written permission from Google. For example, you must not use geocodes obtained through the Service except in conjunction with a Google map, but you may display Street View imagery without a corresponding Google map because the Maps APIs Documentation explicitly permits you to do so. [10.1.1g 27Jan2012]

USPS

User agrees to use the USPS Web site, APIs and USPS data to facilitate USPS shipping transactions only. [27Jan2012]

We make our address verification services available to use for any service. We don't limit how many queries you can make per day and we guarantee that our service will be available. A free API from another service has no incentive to make sure their API is available or even up to date.

Fedex

Use of fedex.com to provide information to or prepare shipments by or for the benefit of third party shippers is expressly prohibited. [Section 2 27Jan2012]

UPS

You may not make, sell, offer for sale, modify, reproduce, display, publicly perform, import, distribute, retransmit or otherwise use the Content in any way, unless expressly permitted to do so by UPS. [Section 2 27Jan2012]