Special Events in Dark Summoner
Special events are time-limited additions to the game. As of this time, the special events that have been seen are:
Stamp collection is essentially a daily login bonus, generally with better rewards as more "stamps" are collected. So far, all stamp collections have had 10 stamps available but run a bit longer than 10 days, meaning you do not have to have 10 consecutive login days to achieve all stamps. Stamp bonuses have included gold, ally points, summons (including Dark Summons and special summons), elixirs, energy and battle point potions and unique monsters.
See: List of Stamp Collections
Social Media Bonus
There are several variations seen in Dark Summoner's Social Media Bonuses. Simply "connecting" Dark Summoner to Twitter, OpenFeint and Facebook give additional daily bonus summons. Also, Twittering a message to view the game's trailer sometimes gives daily bonuses outside the login bonus, and has included Soul Point and Ally Point bonuses.
Dark Summoner has previously had collection missions which were comprised of collecting Orbs, which were randomly awarded for doing regular missions (only uncompleted missions, to keep high-level players from farming 1-energy missions hundreds of times in a row). There were several tiers of award for this, including unique summons, ally point and gold bonuses, and various potions.
As of this time, Dark Summoner had rolled out the Phantom Tower special missions. There are both collection aspects (collecting Relic pieces to obtain a special summon that awards a unique A-tier monster) and player ranking aspects (the highest-ranking players will receive various bonuses), as well as the chance to receive monsters that do not appear to be available during regular missions.