As animal lovers, we are obviously in favour of controlling the number of animals, but we believe that we have moved on from the Medieval peroid enough to make use of sterilisation methods which don't involve traumatic surgery or unpleasent medical side effects. Some alternative sterilisation methods which could possibly be used instead of neutering are listed as follows:  

• If the dosage isn't too high, and if there is enough exposure, X- rays can sterilise males and females completely without causing cancer (if the dosage is too high, then radiation burns and cancer can occure). Microwaves can also be used in this way, but they may only work with males. These methods should also be cheaper then surgery, as well as being less distressing for the animal being sterilised. Recently in the U.S.A., experiments have been carried out on dogs to determine whether it is possible to vasectomise male animals with U.V. radiation. If this method was adopted instead of castration (we don't know whether it would work for females as well) it would mean that there would be no need for surgery, but no one knows yet whether the sterilisation is perminant with low levels of radiation at present, and there are concerns that any radiation exposure can cause problems, so these methods may turn out to be unsafe (we listed them just in case it turns out  they can be used to sterilise animals safely).
• In wolf packs, the Alpha pair are the only wolves that mate. To stop the other females coming into season, the Alpha female uses a pheromone, which, in theory, could be used in a similar fashion to flea collars to stop female dogs coming into season (dogs are, genetically, identical to wolves). This would definitely be cheaper then spaying, and it is much kinder, but it may only be possible to use these pheromones with female dogs, which would mean that its effects would be slightly limited.
• Implants which sterilise female humans for 3 years are in use at the minute, and male versions are being developed. These implants have no other side effects and are implanted with the aid of a local anesthetic. However, unless they could be designed to sterilise permanently, it would be nessersary to make at least 3 trips to the vets for repeated implants.
• This isn't quite the same as sterilisation, but excessive sexual behaviour and aggression in males (if there is a link between hormones and aggression, which is a disputed issue) could be prevented by feeding the animals natural remedies such as lavender, camomile and skullcap with valerian. These cures could be put into petfoods instead of pointless additives which can cause health problems (this should stop the price from going up due to the natural remedies being added to the food). Alternatively, wild yams contain a natural form of  progersterone, which means that, if is was added to pet food, it would decrease the fertility of female animals (progersterone) is the active ingredient in contraceptive pills). In male humans, palmetto can be used to reduce testosterone levels while reducing the humans fertility. It hasn't been tested on animals, but it could be used in pet food as a way of sterilising males (the testosterone-reducing effect shouldn't be sufficient enough to cause the problems which are mentioned in the "Health" section of this website).
• If these methods turn out to be impractical, then vasectomys and tubal ligations could be used. However, these methods are an extreme last resort as, while they don't bring about metabolic and behavioural side effects, they still require traumatic surgery, which should be avoided at all costs. (If you're worried about womb infections in female animals, hysterectomies could be used as they have no hormonial side effects, and they are 100% effective for preventing pregnancies). 
• An alternative to surgical steriliseation for equines is SpayVac. One injection works for 10 years and it doesn't affect the mare's estrogen levels. Tthe problem is that no one is too sure about long-term side effects at present, but, if it turns out to be completely safe, it would make a humane alternative to gelding. Trials are now being conducted with dogs, but it has been proven that SpayVac doesn't work on cats, so it does have limitations. For more information, the website address of the company which produces SpayVac is www.spayvac.org. (Or alterantively, just keep mares and stallions away from each other at all times to eliminate the need for anyone to be sterilised).  
• As far as dogs are concerned, all that the animal's carers have to do is keep their pet on a lead during walks while making sure their gardens are reasonably escape proof. Providing that all of the dogs living in a house are the same sex, and if the dog's carer is responsible, there is no need for any sterilisation techniques to be used at all.
• It might also be possible to sterilise male animals with ultrasound (see http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=966604 for full details).
• Chastity belts could be developed to stop animals from reproducing or passing on S.T.D.s. Assuming that the belt's design was perfect, comfort and hygiene wouldn't be issues (unfortunately, no animal chastity belts exist at the moment, but a lot of companies make them for humans, so there is no reason why they couldn't be developed for animals as well).