If the domains are serving duplicate content, or even similar content with minor variations, you run the risk of being penalized for that by the search engines. At least, that's my understanding from all of the articles I've read.
Irrespective of that, there are many reasons you should be using the
<link rel="canonical" href="..." /> tag in your page in order to direct the search engines as to how to list the official version of the page. Your canonical would always point to one domain even when you're user accessed it from another. If your content is truly identical on each of these domains, this would also resolve the issue of having your content duplicated across those domains I believe (although I've never relied on using canonicals cross-domain).
To be safest, if your content is truly identical, the best policy is to do 301 redirects to your domain which is best-ranked by the engines already. The 301's will tell the engines that all the search equity should be assigned to that one URL. Additionally, when other sites consistently link to your one official site, none of the equity is squandered by being potentially split between different domains. Your DNS provider can probably do this for you by doing domain forwarding.
If your content is not identical, then I don't think there's much you can do besides changing your content strategy to eliminate that and going to a single-domain strategy with redirects.
You should do canonicals even so, but between the two you should be completely covered.