I definitely won't take the fact few people mentions YSOM against Yale. It's still a great b-school; however, as mentioned, it doesn't carry the same prestige as its parent school.
I speculate some of the reasons not many people apply are:
1) It has a small program (>200 student/class)
2) It is a relatively new program, thus has not established the alumni/industry connections as other schools
3) It is well regarded in non-profit, but not a stand out in other fields
But there are also a lot going for YSOM. Nink posted some great reasons (stolen from Nink):
1) Small Class - 200 (expected to increase by 20/yr to about 300 in the next few years)
2) World-class Yale Brand and ability to access Yale, Yale SOM, Yale Law, and other Yale Grad school alums (I networked at Yale Club in NYC with Yale alums before the start of bschool and landed a pre-MBA internship with a well known VC firm)
3) New compelling CORE curriculum - Unique CORE classes such as 'Competitor' (strategy class) and 'Customer' (marketing class), among many others. Innovative integrated curriculum offers a cross-disciplinary approach to teaching and team work is especially stressed. Curriculum is very internationally oriented and Yale's own case department writes cases that are up to date and relevant to the current climate. The Integrated Curriculum continues to be refined and improved with each year, and students can expect to contribute to this process, as well.
4) The Integrated Leadership Perspective capstone is rewarding as students apply the tools and perspectives taught in the core. Joint-degree students with the schools of Forestry and Environmental Science, Public Health, Medicine, Drama, and Law are fully included in the program, providing unique perspectives and opportunities for learning. (Many worthy guest lecturers at every class)
5) Yale SOM is on a quarter system, with the first three quarters dominated by core courses including Economics, Statistics, Marketing, Strategy, Accounting, and Problem Framing. Once the core courses are over, the electives are really the best part of Yale SOM. For example, Tony Blair is teaching. Selected students will be able to take his weekly seminar on faith and globalization.
6) Students can take classes in the law school, international relations Ph.D. program, architecture school, etc. There is a firmly enforced grade non-disclosure policy (GND), and GPA is not calculated. Instead, students are given four possible grades: Distinction, Proficient, Pass, Fail. Distinctions are awarded to the top 10% of students in each class, and nearly everyone else earns a proficient. These grades are not listed on our transcripts (only the courses taken), though students are allowed to list distinctions on their resume.
7) International Travel Abroad requirement included in the first year curriculum - there's significant preparation for the trip, which is led by a faculty member w/ amazing contacts in that respective part of the world that you will be visiting.
8) Employment: Superb East Coast placement. Students are placed into blue chip MBA employers every year. (Small class size of 200 allows better preparation, and service to each student from the school) Year after year, students are headed to Goldman Sachs, Google, McKinsey, Credit Suisse, Boston Consulting Group, JP Morgan, Morgan Stanley, PepsiCo, Proctor & Gamble, Dow Chemicals, etc. (Even in this tough job market, alums and professors are joining in to assist current students to find a job. How great is that?)
Because there are so few students, alumni are not flooded with requests for favors and informational interviews, and they are generally quite willing to lend a hand when they can. On-campus recruiting is strong given the size of the school. Proximity to New York means that banking and finance recruiting is quite convenient, as students can make a quick train ride into the city at any time.
Yale has a lot of prominent healthcare alumni in insurance, investing, hospitals, and healthcare IT. The Career Services leverages alumni in these fields quite well.
Yale is strong and connected in Asia where the brand name is especially prestigious. The best part of recruiting is that Yale's student body is supportive and people work together to obtain jobs rather than compete against each other.
9) Excellent commitment from international alums in supporting SOM, and active international student community. Recent hires in the career services office is allowing Yale SOM to dedicate in facilitating international opportunities for students.
10) Some courses are highly case-based, while others are more lecture-oriented. Several courses use Yale's "raw cases," which require significantly more effort to prepare, but also tend to lead to more in-depth classroom discussions. Elective classes are selected using a bidding process, but the small class size and large pool of faculty mean that usually no more than a handful of classes are oversubscribed.
11) The student body is extraordinarily collegial; without question, the friendliest, most well-adjusted group of business school students assembled anywhere.
12) Student clubs, particularly in consulting, finance, and non-profit fields, offer extensive support for students doing job searches. The consulting club offers one of the most in-depth case interview curricula available, and feedback from employers has been very positive.
13) One of the best part about Yale is that accessibility of its professors. It gives you the small school feeling in terms of care, interaction, and teaching. They are very accessible and help you with academics, career prospects, and leadership development.