Can I submit my site to multiple directories at the same time? Won't the site be banned by Google in search?

I can imagine search engines thinking about your link somewhere in a directory as link exchange and therefore not really increasing your rank when such a link is found, however, I don't see a reason why would they penalize you for having a link to your website somewhere. Perhaps if the directory has a low PageRank, Google might store that information and lower your PageRank in time but I wouldn't really care too much about this. One of the hard part of the off-site SEO is that you can't really control which pages link to you. So my advice would be to submit only to directories relevant to you (local directories or directories with PageRank of 3 and more - use this link to check: http://www.pageranktool.net)