A potential cause of algorithmic deindexing would be excessive downtime. If your site is down for several days it might be removed from the index. There's no hard and fast timeline here but I've generally seen this happen in about 7-10 days at the earliest. When this happens to a site, new links and new activity indicators (pings, etc.) should get it reindexed OK.
Another one would be matching a pattern for a parking page. Google tries to remove common parking pages from the index. I'd guess from your description this wouldn't apply to your site unless you copied a template from a known parking page.
If your site was hacked and had malicious scripts and such on it this could cause deindexing if it's not cleaned up quickly. Webmaster tools will tell you if your site has/had this problem and, once things are taken care of, you can request reconsideration.
Your site might have been given a visual review by a Google contractor and was marked as a spam or thin affiliate site. If you were showing a lot of ads and such or match other patterns common to "Made For Affiliate/Adsense" sites this could have gotten your site flagged. If this is the case, then you'll need to clean up the site to fit guidelines and request reconsideration via Webmaster Tools.
EDIT TO ANSWER COMMENT
It's possible that it was deindexed previously. It could be simply for being a parking page or a down/inactive domain. It could also be something worse.
It's quite rare for a site to be deindexed due to inbound links alone. It would have to have been part of a paid linking scheme that was manually detected and eliminated. Even then, there would have been outbound links or perhaps other indicators to tie it directly to the scheme.
Google Webmaster Tools will be your best resource for determining the reason why it's deindexed. If the cause is it being marked inactive, take steps to make sure Googlebot knows it's active again and it will get reindexed within a few days, perhaps a little longer. If there's a penalty deindex, request reconsideration, explaining that you're the new owner of the domain and that you are not associated with the prior owner. This can take a while though. While I've had some requests take less than a month, I've had others take nearly a year.