I'm an alliance leader. On a daily basis I'm faced with that very same problem

Not that I see " I'm Bored" very often but I dread the few times that I do. And usually it sends me into an involuntary typeing frenzy trying to outline/remind people of all the things that are available to them if they bother to register on the forums
Heres a link to our forums
http://rawralliance.forum2u.org under the " Alliance Events " section you can see all the things we try to keep things fresh and fun.
Our Friday night Lotto is our monster event

With prize pots always around 60-70k in gold and 30-45 donated gold/green items
Our Scavenger Hunt is still in its infancy but growing every week.
Also on the back burners are......
Dodge Ball ( i vote for 1 person with correct runes/skills and the rest of us running around nekkid and drunk )
Alliance wide trivia ( wiki has TONS of useless trivia )
Guild relay races in a Guild Hall ( racing along a pre-set path and trading a mini pet to each team member )
Hide n Seek ( using alliance guild halls )
Bingo ( using /roll command )
Get Rich Fast ( party into an explorable area, 1 person drop 500-1000 gold pieces 1 at a time, the others race to pick up as many as they can, gold/green items as well as mods/inscriptions also work )
UAC ( Ugly Armor Contest, find the worst, mis-matched,ill-fitting,disgustingly dyed, noobest, ugliest event mask and put them all together : ) lol Have guild/alliance members vote for the best of the worst armor )
and heres one example of the thought we put into an event..........
P2P Racing ( portal 2 portal )
A group of racers all form a group in an outpost or town. Depending on the number of racers different outposts that allow larger groups may be needed. A " judge or referee" joins the group. Upon exiting to the explorable area the " judge" promptly " dies". Much to the enjoyment of the competitors who seeem to enjoy watching him/her rush headfirst nekkid into the 1st group of monsters that volunteers to violate said judge.
Then with a " GO " command in Alliance or team chat the race is on. Different strategies can be used. The usual " Bum Rush" and see who lives or a more tactical "agrro everything and scrape them off on an unsuspecting victim" seems to be a favorite. People can work together or fly solo. Its really up to them

A running play by play in alliance chat is also good for moral and for generating intrest for other players.
The judge can see if someone zones or leaves the party which is instant disqualification and jump around from racer to racer to check progress or laugh at failure

Its all in good fun and so far we havent gotten it rolling but hope to in the near future.
1st person to enter next town/outpost is the winner.
Thats 1 example of something we are trying to get started. On our forums are several more original ideas and a few borrowed from other guilds.
Hope this helps and best of luck
Once again heres the link to our forums
http://rawralliance.forum2u.org
Everyone is more than welcome to join/post on our forums
My ign is Dies Fourth feel free to pm me with any questions or if your intrested in a solid mature family friendly guild/alliance : ) It may take me awhile to answer though so please be patient.