I'm going to take this opportunity to plug Nathan Winograd's blog because I feel very strongly that he's on the right track when it comes to animal welfare and reducing the number of animals killed in shelters each day.
The average person doesn't have any idea how shelters are really being run or what's wrong with the system. Winograd's works are a good introduction to that world and what really can be done about it. We do not have to kill nearly as many animals as we do each year, there is a humane solution and it is not limited to just spay and neuter programs.
You may also want to check out his book, Redemption.
Before you journey into this world, I should warn you, there is a polarizing battle going on between animal rights and animal welfare organizations, and what most people don't know, is that there is a significant difference between the two.
To keep this short and sweet, but certainly not without my own bias, animal rights refers to organizations such as PETA, The Animal Liberation Front and the Humane Society of the United States (which has absolutely nothing to do with your local humane society shelter). These organizations raise a great deal of money and spend almost all of it on advertising, programs to promote veganism (even for our carnivorous pets) and to influence law makers. The HSUS does not operate a single shelter, anywhere, yet they raise millions every year and have one hell of a PR department. PETA, raises millions per year and is under investigation by the FBI for fraud and terrorist related activities, they own one shelter, where the kill rate is over 90%. Remember all that money PETA raised to help the animal victims of Katrina and Michael Vick's pit bulls? Yeah, if you read the fine print, that doesn't actually go to rescue and rehab efforts, it gets reinvested into public education programs, like when PETA does presentations in public schools to promote veganism and discourage pet ownership, or like when they handed out "buckets of blood" to children as they left KFC restaurants, or the development of video games that promote their ideals. The ALF is a known terrorist organization with very close ties to PETA, that proudly proclaims they support violence against humans as an acceptable method of coercion in the "liberation" of all animals. Incidentally, these organizations have members who have released people's pets from their crates or fenced in enclosures and/or killed well loved and cared for pets in the name of "liberation". The leaders of these organizations have publicly declared that they seek the extinction of the domestic animal .. no more pet ownership period. No working dogs, no police dogs, no service dogs, no search and rescue dogs. They would like to achieve this through mandatory spay/neuter laws, and breed specific regulation (outlawing just about every breed of cat and dog you can imagine) that in the course of a few generations would eliminate pets. By the way, they also want to eliminate livestock and have all humans subsist on a vegan diet. You can also forget about insulin for diabetics and most medical research and technology. These organizations support legislation that would make you the guardian of your pet rather than the owner, which at first glance sounds sweet, but what it really means is that you give up your rights to that animal, your right to decide what is best for your pet, what to feed them, what kind of veterinary care to get, whether they are spayed or neutered, whether you compete in dog shows or sports, whether you dog wears a sweater and boots or not. Guardianship means that you and your vet may not be the ones who decide when it's time to humanely euthanize a suffering pet. It means that someone could sue you on behalf of your pet for perceived abuse. Before you nod your head, thinking that's a good thing, remember all of the nut cases out there. Recently a man was turned in to animal control for taking his healthy, happy, energetic, hunting dog running with him (off leash, the dog was running of his own free will), the accuser stated that dogs should not run, and to let them do so is tantamount to abuse (Every vet, breeder and animal trainer on the planet just cringed in unison). Animal control dealt with the crackpot appropriately, but keep in mind that if animal guardianship comes about, those kind of claims will have to be taken seriously under the law.
Animal welfare refers to anyone interested in preventing animal abuse, promoting responsible ownership and running no/low-kill shelters and rescues. These are the moderates, the people who truly love animals, who keep pets of their own, who save lives. These are the people who spent their own money and risked their own lives entering New Orleans to rescue cats and dogs before it was too late. These are the people who are deserving of your donations, volunteer efforts, moral and political support.
Now, if you don't believe me, want citations, want to read the same information in a coherent format :) or just want to learn more, I'm going to provide you with a very short list of links, just to get you started. A quick Google search would probably give you enough reading material to keep you busy for the next ten years ...