Involvement in extracurricular activities is viewed very favorably by a veterinary school admissions committee, for if you can maintain a competitive GPA and still have the time and energy to actively participate in extracurricular activities, both your aptitude and motivation must be rather high.
That said, there is no particular benefit in being simply a member who never participates or becomes involved in an organization; instead, if you have been very active, particularly if you have held office or in some other way present evidence of your leadership, you will usually be considered as the most competitive and attractive candidate for vet school.
You do not have to be involved in variety of different organizations or only those that are geared towards careers in healthcare. On the contrary, it is advised that you find a couple of extracurricular activities or student organizations about which you are very passionate and try to get as deeply involved as possible. Consistency and active participation are prized by admissions committees over simply the number of things you are involved in. By choosing quality over quantity, this will also keep you from spreading yourself to thin, which can inadvertently affect your GPA.
Further, your activities do not need to be strictly health related. In fact, a great many successful pre-vet students at UGA join social fraternities and sororities, take an active role in various service and religious organizations, play varsity or intramural sports, participate in debating societies, theatrical groups, the band, etc. Others participate in student advisory and leadership roles on campus, such as the Arch Society. It is your participation and interest in these activities that are important, not the specific focus.
A list of Pre-Health campus organizations can be found here.
Finally, it must be emphasized, that no amount of involvement in extracurricular activities can substitute for a good academic record and strong GRE scores.
