If it's true the "most popular" clinics are hard to get into, which are they?
None of the clinics are easy to get into. Probably less than 20% of 2L applicants get into a clinic, and almost no one will ever get to take more than one clinic.
The only clinics it is possible to get into if you don't rank them #1 are the street law clinic and the law students in court clinic. Basically, it seems like you only have a real shot at taking a clinic as a 3L, and then you only have a shot (thought it's a pretty good one) at your #1 ranked clinic.
I think you may be overstating it a bit. Some clinics have a policy of only allowing 3Ls, either officially (Appellate Litigation) or unofficially (Institute for Public Representation, Federal Legislation), while others like Criminal and Juvenile Justice, Domestic Violence, and Law Students in Court all require Evidence as a prerequisite (which locks out rising 2Ls). The immigration clinic gets the most applicants and is hardest to get into statistically, but it does accept an even number of 2Ls and 3Ls. The Harrison Housing and Harrison Policy Clinics and International Women's Human Rights Clinic all accepted quite a few 2Ls this year. But you do need to carefully target the clinic you want, make it your first choice, and put together a strong application. Especially as a 2L, but some 3Ls get shut out too.
Once you do a clinic as a 2L, you go to the back of the line if you apply for another as a 3L (they want to give as many people as possible the chance to do at least one).