I get annoyed by that as well; normally, I will send back what they sent with a note saying, "I would appreciate it if you would spend my money on the animals, not on these promotional items. Please do not send me any other materials; I will donate as I see fit." Most groups I've done this to listen for about a year (lol). Then you need to remind them again. You can demand to be taken off of their list, as well, but if you donate to other charities, it will find a way back on there again; animal charities share their lists with one another.
HSUS is a great group, but frankly, they have a huge funding base - enough to send out gratuitous items to guilt trip people into donating. Perhaps you could only give them say, an annual gift, around christmas or something? Small groups are where the money is needed, and I'm sure there are many in your area you don't even know about! Most local shelters have a "wish list" of items - these are so very important, but most people send money. Sending items saves time volunteers have to spend buying the stuff, which gives them more time to spend on animals. In fact, the biggest commondity that shelters have the least of is volunteers! So if you want to help out, volunteering either on or off site is a wonderful way to pitch in.
Also, if you want to support large groups, but ones that don't send as much stuff, I'm pretty sure
WSPA only sends newsletters and action alerts. They are a massive international organization; they do a ton of disaster relief, crack down on illegal exotics smuggling, hold vaccination clinics in 3rd world countries, etc. So they are a spectacular group to help support.
Here are links to other groups you could look in to. They all focus on different issues, so you can choose which one is true to your heart:
The Fund for Animals < Lots of focus on wildlife, but all animals are covered. Considered more of a "rights" organization than a welfare group, but they do a lot with legislation, and operate two major sanctuaries.
ASPCA < One of the oldest and best established groups in the US. Welfarist. Do legislative work, and operate or oversee many animal shelters. You may have seen thier NY headquarters on "Animal Cops: NYC"
Best Friends Animal Society < A simply wonderful Utah-based welfare group. Focus is on domesticated animals, and native wildlife. They operate a MASSIVE sanctuary in Utah - largest in the nation for domestics. They have a foot-in on many legislative issues, and sponsor adopt-a-thons and spay/nueter clinics for other, less funded groups. They do not send much crap, either; you get a cute magazine, and occasional newsletters.
Animal Legal Defense Fund < A group focusing entirely on legislature. They are responsible for backing and pushing recent bills, such as banning the slaughter of downed cattle, strengthening punishments for animal fighting, stopping the transport of big cats over state lines, ending Foi Gras force-feeding cruelty, etc. Mixed rights/welfare group.
Others maybe worth checking out would be IDA, API, UPC, etc. However they are much more focused on specific issues, and may be mostly education based as opposed to rescue-based.