In the early 1980s, there was a renewed push to form an incorporated World Science Fiction Society ("WSFS Inc.") that would, among other things, hold title to the intellectual property of WSFS including The Hugo Awards. There was much debate, committee meetings, bylaws drafting, etc. In the end, nearly all of it was set aside and left unimplemented. However, some of the things in it did make their way into the current WSFS (an unincorporated literary society) Constitution. Among them was something called the "Standing Committee," which I think was based on what would have been the Board of Directors of WSFS Inc. It consisted of members elected by the Business Meeting and appointed by past and future Worldcons. If this sounds familiar, it's because the organizational descendent (via two different name changes) of the Standing Committee of WSFS is the WSFS Mark Protection Committee, of which I'm currently Chairman.
The Standing Committee/Mark Registration and Protection Committee/Mark Protection Committee proceeded to register (in the USA, with the US Patent & Trademark Office) service marks on "Hugo Award," "Worldcon," and other names associated with WSFS. A couple of them were rejected ("Science Fiction Achievement Award", "North American Science Fiction Convention") as too generic (that's one of the reasons why WSFS changed the official name of the Hugo Award to "Hugo Award"). In the past few years, we've added to that stable of service marks with the Hugo Award Logo (accept no substitutes!) in 2009 and the distinctive design of the Hugo Award trophy rocket just this past year.
Obviously, we don't claim protection on every sort of rocket shape there ever was, only rockets of our sort in the context of awards for achievement in the field of SF/F. Similarly, we don't claim exclusive rights to the name "Hugo" in every possible context. That would be stupid. WSFS doesn't make high-end designer clothing or perfume. Hugo Boss doesn't give out SF/F literary prizes. Trade and service marks are limited in their protections. (IANAL; consult an IP attorney for real legal advice.)
There are existing awards that have the word "Hugo" in their titles. I'm not going to list them because frankly I don't really want to give them any more notice than they already have, but some of you send me pointers to their announcements every year when their awards come out. At least one of them has sufficient history to have carved out their own namespace, and we have an agreement with them to not overlap any more than we have to do so. I note that people tend to contact the Hugo Awards web site when those other awards come out because we appear to have done a better job of turning up in search engines.
Other groups that might overlap more closely into WSFS's literary awards have from time to time launched awards that might cause confusion. When we spot them, we try to warn them off. Sometimes (rarely) this requires us to ask our paid attorney to write polite-but-firm letters and negotiate with potentially-conflicting users. We try to give people ways out when we can do so, steering them into names that include the word "Hugo" but not the phrase "Hugo Award."
WSFS has never sued anyone for any reason, including service mark infringement, nor has it been sued by anyone for any sort of infringement itself.
WSFS (through the Mark Protection Committee) wants to claim its marks worldwide. In practice, we have a policy of pursuing registration in any country (the EU counts as one "country" for this purpose) that has hosted more than one Worldcon. However, this leads to a further complication, in that while the US Patent & Trademark Office will (grudgingly) agree to issue registrations to unincorporated societies, we've found that it's practically impossible to do this anywhere else. The equivalent agencies in Australia, Canada, and the EU (including the UK) want either individuals or legal entities, and don't consider unincorporated societies to be legal entities. Therefore, the MPC asked for guidance from last year's Business Meeting, and based on an advisory motion, has been working on creating a legal entity (which will not be called "WSFS Inc."!) that can legally hold title to the marks in a way that the non-US agencies understand. I hope to have a full report on that for the MPC's report to this year's Business Meeting. Once that's accomplished and we've lined up funding, the MPC can start registering the marks in those other regions/countries.
I hope this clarifies what the status of the WSFS service marks on "Hugo Award" and the others is. So far as I know, registration was not initially pursued because of an active or threatened infringement directly upon the name of the Award, but proactively to make it much less likely in the future and to protect the collective interests of the members of Worldcon.