College admissions for homeschooled students

"Standardized test scores hold relatively more weight for home-schooled applicants. If you are a home-schooler and you feel confident about your ability to do well on the exams, we advise you to demonstrate your abilities in various areas by taking more than the required two SAT Subject Tests." (Yale)
"We find that in most cases, homeschooled applicants are no more difficult to evaluate than any other applicants to Caltech, and there are no additional requirements for homeschooled applicants." (Caltech) "Evaluation is usually difficult, however. It helps if the applicant has taken some college level courses, and we can get evaluations from those teachers." Yale. Some claim that Yale is unusually
AP scores may help.
There should be evidence that you can integrate well with other students
Taking courses at a local college can facilitate getting credible letters of recommendation.
Study all of the standard subjects.
Documentation can be important – reading lists.
Home-schooled students constitute a very small minority of students at elite schools, e.g. of Princeton students even though ~3% of students are home schooled nationwide. Possible selection effects:

More / Fewer homeschoolers applying / attending than usual. MIT says that fewer than 1% of applicants homeschooled.
Homeschoolers being better / worse than average.
Some homeschoolers not properly documenting their coursework, etc. or taking extra SAT subject tests.

"While not an ivy league, I know UChicago has 13 freshman who listed themselves as homeschooled on a survey we had to fill out at the beginning of the year." (Total class size of 1,426, so 1%) http://talk.collegeconfidential.com/home-schooling-college/874682-homeschool-students-admission-rate-to-harvard-princeton-yale-p3.html

It's said that getting into University of California schools is difficult as a homeschooler (perhaps moreso than Ivy League schools). See University of California and homeschoolers for more information.

Greater flexibility in how one arranges one's coursework, schedule could mean more ability to optimize activities so that you do well in them (e.g. can pick your own textbooks, etc.) Having a good reason for homeschooling might help. New York University Princeton university Columbia University University of Chicago Caltech Highly Selective College Admissions for Homeschoolers

Home Schooling and College at College Confidential Homeschool students' admission rate to Harvard/Princeton/Yale How do homeschooled students attend Ivy leagues? MIT