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There are several banks you can apply to for loans online. The question is, what type of loan? Is your friend looking for a personal loan, mortgage loan, car loan? I have applied online for all three, and have had good experiences (and better rates).
My favorite was ebank, which has since closed and is now owned by Stearns Bank (they had really low closing costs and quick closings on their mortgage loans). You can apply for a Bank of America personal loan, car loan or mortgage online. Also, you can apply for car loans through companies like E-Loan and Capital One Auto Finance. If you're more specific on the type of loan, I can give you more examples. Also, www.bankrate.com is a good source for bank loans.
Depending on the type of loan you apply for, they will either send someone out to you (for instance with a mortgage) to close the loan after your online application, or they will have you email, upload to their website and/or mail the documents they need from you, and you will have to get documents notarized (i.e. with a personal loan or car loan).
Source(s):
Personal experience - good experiences applying for car loan, mortgage and personal loan online.