Of course!
Check out the Google forums; you'll find thousands of people asking for various reconsiderations.
De-indexing usually only happens where a site is doing massive outbound linking (link farms) or where there is a combination of negative factors like: Very low quality content and layout, linking to and from 'bad/spammy neighbourhoods', and bad advertising/legal practices etc.
Penalisation normally happens from over-optimisation of keyword terms or overly aggressive linking, and usually only affects those specific search terms. i.e. You've built hundreds or thousands of links to a new site, all with the same exact anchor text, which is also in the site URL (An EMD/PMD - or Exact/Phrase Match Domain), and it's in the Page Title, H1 tags and loaded into the content too. This is the ideal example of a newbie mistake in online marketing; thinking that more is better.
A 'Google Slap' is the industry lingo for either a broad sweeping change/update in their algorithm which affects a lot of sites, or when a single person/business gets hit by Google for practices they consider outside of their TOS (Terms Of Service), and this is often associated with the AdSense program and AdSense sites.