In a completely unscientific poll of 123 LinkedIn users I conducted about two hours ago, I found they overwhelmingly prefer the online channel over all others when accessing bank transaction data (see notes 1, 2, 3).

I was expecting mobile to be higher. But unless you have a new-generation smartphone and your financial institution supports mobile, it's unlikely to be your first choice. So given that mobile's only been widely available in the United States for about a year, a one-in-ten preference is a strong start. 

I also expected a bit more interest in the other choices: ATM, voice and social network, which only drew 3% of responses in total. Social networks went 0 for 123, showing that it's not yet viewed as a place to review financial data (note 4), at least among LinkedIn users. In a much differently worded poll of Facebook users a year ago, we found that 13% willing to view their bank balance within the social network.

Notes:
1. The question is strictly limited to 75 characters, I couldn't make it as precise as I would have liked. For instance, I would have like to add "assuming its secure" and "your personal" to "transaction data." It's possible some respondents were thinking more about global banking data than their own personal transactions. The poll also displayed "by Jim Bruene, Owner, Online Banking Report" in the lower-left, potentially biasing results.
2. LinkedIn users are given opportunities to respond to polls while logged in to the service. There is no financial benefit to taking the survey, but they do get to see results after taking it.
3. There were significant differences based on demographics, for instance women were almost twice as likely to select "mobile." And zero men, and 4% of women, chose voice call as the preferred method. But due to the small sample size, these demographic breakdowns don't hold much weight. There also appears to be some mathematical errors in the demographic splits, so I'm not going to cite them further until Linked:in cleans up it algorithms.
4. An interesting result, given the poll was conducted within a social network among social network users. Actually, "the branch" beat social networks, drawing one "write-in vote" in the poll comments (it was not one of the five choices). 
5. For more info on mobile banking see our latest Online Banking Report on Mobile Banking 2.0 -- iPhone Edition.