Software patents are the lightning rod issue of the moment in free software, because they pose the only real threat against which the free software community cannot defend itself. Copyright and trademark problems can always be gotten around. If part of your code looks like it may infringe on someone else's copyright, you can just rewrite that part. If it turns out someone has a trademark on your project's name, at the very worst you can just rename the project. Although changing names would be a temporary inconvenience, it wouldn't matter in the long run, since the code itself would still do what it always did.
But a patent is a blanket injunction against implementing a certain idea. It doesn't matter who writes the code, nor even what programming language is used. Once someone has accused a free software project of infringing a patent, the project must either stop implementing that particular feature, or face an expensive and time-consuming lawsuit. Since the instigators of such lawsuits are usually corporations with deep pockets—that's who has the resources and inclination to acquire patents in the first place—most free software projects cannot afford the latter possibility, and must capitulate immediately even if they think it highly likely that the patent would be unenforceable in court. To avoid getting into such a situation in the first place, free software projects are starting to code defensively, avoiding patented algorithms in advance even when they are the best or only available solution to a programming problem.
Surveys and anecdotal evidence show that not only the vast majority of open source programmers, but a majority of all programmers, think that software patents should be abolished entirely. Open source programmers tend to feel particularly strongly about it, and may refuse to work on projects that are too closely associated with the collection or enforcement of software patents. If your organization collects software patents, then make it clear, in a public and irrevocable way, that the patents would never be enforced on open source projects, and that they are only to be used as a defense in case some other party initiates an infringement suit against your organization. This is not only the right thing to do, it's also good open source public relations.
Unfortunately, collecting patents for defensive purposes is a rational action. The current patent system, at least in the United States, is by its nature an arms race: if your competitors have acquired a lot of patents, then your best defense is to acquire a lot of patents yourself, so that if you're ever hit with a patent infringement suit you can respond with a similar threat—then the two parties usually sit down and work out a cross-licensing deal so that neither of them has to pay anything, except to their intellectual property lawyers of course.
The harm done to free software by software patents is more insidious than just direct threats to code development, however. Software patents encourage an atmosphere of secrecy among firmware designers, who justifiably worry that by publishing details of their interfaces they will be giving technical help to competitors seeking to slap them with patent infringement suits. This is not just a theoretical danger; it has apparently been happening for a long time in the video card industry, for example. Many video card manufacturers are reluctant to release the detailed programming specifications needed to produce high-performance open source drivers for their cards, thus making it impossible for free operating systems to support those cards to their full potential. Why would the manufacturers do this? It doesn't make sense for them to work against software support; after all, compatibility with more operating systems can only mean more card sales. But it turns out that, behind the design room door, these shops are all violating one another's patents, sometimes knowingly and sometimes accidentally. The patents are so unpredictable and so potentially broad that no card manufacturer can ever be certain it's safe, even after doing a patent search. Thus, manufacturers dare not publish their full interface specifications, since that would make it much easier for competitors to figure out whether any patents are being infringed. (Of course, the nature of this situation is such that you will not find a written admission from a primary source that it is going on; I learned it through a personal communication.)
Some free software licenses have special clauses to combat, or at least discourage, software patents. The GNU GPL, for example, contains this language:
7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. [...] It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice.
The Apache License, Version 2.0 (http://www.apache.org/licenses/LICENSE-2.0) also contains anti-patent requirements. First, it stipulates that anyone distributing code under the license must implicitly include a royalty-free patent license for any patents they might hold that could apply to the code. Second, and most ingeniously, it punishes anyone who initiates a patent infringement claim on the covered work, by automatically terminating their implicit patent license the moment such a claim is made:
3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed.
Although it is useful, both legally and politically, to build patent defenses into free software licenses this way, in the end these steps will not be enough to dispel the chilling effect that the threat of patent lawsuits has on free software. Only changes in the substance or interpretation of international patent law will do that. To learn more about the problem, and how it's being fought, go to http://www.nosoftwarepatents.com/. The Wikipedia article http://en.wikipedia.org/wiki/Software_patent also has a lot of useful information on software patents. I've also written a blog post summarizing the arguments against software patents, at http://www.rants.org/2007/05/01/how-to-tell-that-software-patents-are-a-bad-idea/.
 Sun Microsystems and IBM have also made at least a gesture at the problem from the other direction, by freeing large numbers of software patents—1600 and 500 respectively—for use by the open source community. I am not a lawyer and thus can't evaluate the real utility of these grants, but even if they are all important patents, and the terms of the grants make them truly free for use by any open source project, it would still be only a drop in the bucket.