Special and Seasonal Events
City of Heroes is not just going through the streets pwning bad guys day after day--every so often, a special event pops up to give heroes a unique challenge. Whether it's Halloween trick-or-treating at mission doors, taking down the Kraken in Perez Park, or flying through hero zones to find presents during the holiday event, special and seasonal events add a necessary spice to everyday leveling.
Hero Zone Special Events
These events consist mainly of invasions, weird zone events, or special Giant Monsters that occasionally rampage through hero zones in the midst of regular missions, scaring the NPCs and endangering heroes who are not high enough level to deal with them. Rikti and Zombie invasions can strike in any zone; Giant Monsters are generally confined to one zone.
If you're looking to exploit these events for XP purposes, first remember to turn on the Hero Zone Event Messages in your Chatbox. Right-click the Chat tab you want to add it to, select "Edit Tab" and then select "Hero Zone Event Messages" from the right side of the dialog box if it is not already a part of your Chat tab. This will alert you to when Giant Monsters appear or when special zone-specific events happen (like Steel Canyon building fires, etc.).
Second, remember not to try to solo the special event. No one hero can do enough damage to a Giant Monster to even scratch it, not even if you're level 50. No one hero can take on a Rikti or Zombie invasion by themselves--they'll get overwhelmed. Assemble a team of 8 people, and put out a Broadcast and Request message to any other heroes who may be in the zone to come and help. Several teams of 8 people each can do some great damage to Giant Monsters, put out the Steel Canyon building fires, break up a Troll Rave in Skyway City, and bust a few Ghosts from the Ghost Ship in Talos Island and Independence Port. Large groups of heroes can also make fairly quick work of Rikti and Zombies--just be prepared to stand there blasting/punching/buffing/healing for a good while!
A quick note about Rikti and Zombie Invasions: Look to the skies for warnings of incoming invasions! An ugly mustard-yellow shade in the sky heralds a Rikti invasion; a violent purplish-red shade indicates incoming Zombies.
If one of these events begins while you're in the target zone, and you don't want any part of it, get yourself either into a mission building, or into one of the following "safe" buildings: City Hall, Hospitals, Wentworth's, AE Buildings, Vanguard buildings, Police Stations, Train Stations, and Stores that aren't just people standing in the street. If you get killed in the process of trying to get there, just stay in the Hospital until you see a message in the Hero Zone Event Channel reading something like "Everything's back to normal."
The ParagonWiki article on Hero Zone Event Messages goes into more detail about the different zone events. Check it out to find out much more!
Seasonal Events
During the year, special events related to the time of year outside the game happen, such as Halloween trick-or-treating, defeating the Winter Lord and saving Baby New Year, and helping the forces of l'amour triumph.
The same basic guidelines I mentioned in terms of Hero Zone events applies here: don't attempt any event by yourself, keep tabs on your Hero Zone Event Messages, and read up about each upcoming event as the developers make announcements about it. Since the seasonal events are slightly different each year, this will be the best way to have up-to-date information.
ParagonWiki's page on Seasonal Events will help you learn about past seasonal events as well as keeping you updated on possible future events.