It depends greatly on the type of traffic that you're serving, but there are a number of ways to mitigate. (I'm going to assume Web sites.) A relatively simple and inexpensive way to solve this is by putting Varnish (or another http cache) in front of your web servers. This will reduce the number of traffic hits that make it to your web and app servers greatly. Also, using a product like HAProxy as a load-balancer can help somewhat by managing the distribution of your http traffic to your servers.
There are DDOS-preventing measures available, but are going to be expensive. I know that if you are using Rackspace for hosting, they have a product offering called Preventier (which I know to be expensive.)
It could also be worth your time to leverage Akamai (or similar CDN) to host your content, which will also solve this problem, but typically has a high dollar-cost.
As in all things, a risk vs reward analysis must be performed, but you must keep in mind that beyond your service availability, you're also essentially paying for your brand's reputation.
NOTE: I say inexpensive for Varnish and HAProxy because, while they are Free/Open-Source, it does have a cost in engineer-hours to implement and support. Note that this is true of any solution, but these have a zero-dollar licensing cost.