If you just blindly go through your classes, no professor is ever going to know your name. There are just too many people in the classes usually, especially the intro classes or required classes for science majors. There are some freshman seminars that have limited enrollment to encourage professor/student interaction, but there is usually little reason to have a bond after the class is over. However, I did get to know a few professors well through being the tutor for their class or through showing interest in their subject.
Most students start out as bio majors, and by the end, most of them end up in other majors either because they couldn't cut it or because they weren't that interested in the subject. As a result, non-science majors get a lot of the science (and also some engineering) rejects. Students aren't usually too aggressive with the exception of the premed people, which constitute a large proportion of the school and of the bio majors. Although I never experienced having notes stolen or pages torn out of books as I've heard from other institutions, the premed people are pretty hard core about making the grade, establishing connections with professors for letters of recommendation, getting in the extracurriculars, etc. Many classes also grade on a curve, which can encourage competition, but I was always helped by the curve.
Biology is a very popular major at UCI as the majority of the students start out wanting to be doctors. As the years go on, though, many realize they may not have the stamina to do so, but at the end, a lot of people do end up following through to medical school. If you don't have priority at registration, it can be hard to get the classes you want, but there are waiting lists. Academic advising can be hit and miss in the biology department. A few of the academic counselors have been very helpful to me, but everyone I've talked to has had some traumatic experience in the biology student affairs office. With the huge number of students they serve, I can kind of see how that could be, but they can be kind of harsh if you're not the best student.
Most of the professors are very accessible with office hours and through email. On-campus housing also makes a conscious effort to get professors into the housing complexes to interact with students. However, most students probably have very little interaction with their professors outside of class time. On the other hand, if you engage in undergraduate research as I did, you'll probably develop a very strong relationship with that professor with whom you do research. I know I've been out to eat with my PI (principal investigator=head of research lab) several times and have kept contact with her even after graduation.
UCI has a laundry list of breadth requirements, which are kind of a hassle, but I suppose they are a necessary evil. Probably the most well-known breadth class is Humanities Core Course, which is a year long class that involves reading lots of literary works and writing lots of papers but also fulfills a lot of requirements. The school builds it up to be a great thing, and I suppose if you're into the humanities, it is. If you don't really like all the reading, writing, and analysis, it's really not that great. I guess I strengthened my writing skills, but I wouldn't really recommend it to someone unless they did like the humanities.