Depends what sub-field of neuroscience you are interested in/what type of work in that field you want to do.

Biology, microbiology, etc. are good but there are many, many other people from these backgrounds applying to graduate programs in neuroscience.

If you're interested in the more mathematical/modelling side of neuroscience having an undergraduate degree in math, computer science or even physics will get you pretty far because many research groups and programs are starving for good computational people. And, in my opinion, it's much easier to learn the biology after studying math/computers than the reverse.

I wouldn't recommend psychology programs as much since you won't get as much hard science under your belt, and current neuroscience needs a wide base of basic science. Also, psychology programs tend to be very large and you might have a tough time getting in a good position to apply, since it's harder to have contact with profs or work in research labs when you're in undergrad. And again, you'll be one of many from psychology undergrad programs to be applying to neuroscience grad school.

Since many neuroscience graduate programs are interdisciplinary, you have a lot of freedom in choosing a major. You can start from the chemistry side, biology side, or like me, the biochemistry side. They don't really care as long as you are well versed. Also, if your university has electives that deal in psychology or neuroscience I would try to take a couple to show that you are interested and have some knowledge of the field.

You could joint major in psychology and biology or psychology and biomedical physiology.

Yeah, enold4mizzou is right. Biology, chemistry, biochemistry, microbiology. These are all good choices. I just got into UNC Chapel Hill for neurobiology from a Psychology/Philosophy undergrad, but admittedly, not many students from these majors will get accepted to neuroscience programs.

I agree with the comments about going into biology/chemistry/psychology but I would like to add that with these non-neuroscience majors you might need to buffer that up with more neuroscience-based modules. For example, I was a psychology undergrad, but I took a lot of cognitive neuroscience modules and expressed an interest in neuroscience, which led me to a RA-ship at a neuroscience lab. I picked up my neuroscience biology and computational skills during the past two years working, which gives me a better chance at applying for neuroscience graduate programs. Let your professors know your intenttion early, and they will try to get you research opportunities (both at undergrad and post bachelors level). Work for well known neuroscience professors. do well in your GREs. These are all advice I got from people who have done the same as me, who are/were all in neuroscience graduate programs.

I'll let you know in about 7 months' time how that's working out for me. :)

My undergrad had a neuroscience program for only 20 people and 300 apply. I didn't get in but double majored in Biology and Cognitive Science (which includes neuroscience, cognitive psychology, linguistics, computer science and philosophy). Any of these fields would be good depending on your interests. Major in anything you like and take some hard science classes (molecular/cell biology, biochemistry, or genetics) and you should be fine.

My friends who interviewed for neuroscience grad programs said they saw many engineering majors so that might be a good route if you're up for the challenge.

I would have never taken linguistics classes if it weren't for cog sci and it became a passion of mine, so be open to new things!