In relation to other professions on this board, admissions is far easier. However, there is no guarantee, especially if you attempt to get a MSW initially with no social work experience. If you are going to well known schools, there will be increased competition. To be frank, it changes every year. Your best bet is to call the person in the program who deals with admissions and such, to find out what they are looking for. If you already have social work experience, it will really help, even if you do not end up going in as a advanced standing student. You may actually miss out on a lot, such as getting to know your cohort and actually getting some time to let some of the material sink in.
The amount you apply to really depends on a lot of stuff, such as your past experience, if reputation matters, and your grades. If you are only applying to the top ranked social work programs, I would apply to at least 5; it will be a lot of admissions work, but you do not want to wait another year as many of the best programs have static admissions. If you are applying to state, private, and less well known schools, you can probably get away with applying to less as there should be room.
Hemingway12, you will have to look at the school department websites to see if your GPA hits their minimum. Those schools usually have a minimum that even the department director cannot override due to policy, even if you have substantial experience. Talk to the individuals in the program that deal with admissions as well, you can most likely compensate that GPA with a good GRE, statement, and maybe even interview. While there is a growing trend for more social work programs becoming more clinical, many still utilize a more holistic approach to admissions.
Social work Ph.D programs are a bit of a different animal. Many want some real world experience before applying, some prefer a MSW before application, but the most important thing is that you have some research experience before application (I have yet to see anyone with social work research experience get denied). This can be acquired through research practicums in a MSW program. Having said that, research is a completely different path than what is usually offered in practicums in a BSW/MSW program. Also, your job prospects will be much more "focused." While you will be able to teach at universities and get tenure and maybe apply to some research/leadership positions, the vast majority of social work jobs will not be within your grasp. It is not like psychology, where the Ph.D is sought after. While you guys are applying to social work schools, not only talk to the social work department regarding admissions, but also talk to some of the professors that specialize in research. Who knows, this could help you get into the program.
Last but not least, make sure the programs you apply for specialize in the parts of social work that you want to delve into. It can be very difficult to escape a practicum to find a more suitable one mid semester, with your self respect intact and transferring mid program can be absolute hell (you would think that there would be some academic conformity but there is not). There is a lot more that I would like to discuss, but this post is already turning into a wall of text. Pm me if you have anymore questions, I hope this has helped you in your pursuit.