Here are some things I have done in the past with my guild:
Mystery Item: Place an objects picture up and let the members guess what they are. Make sure you save it to your server or they can just look at the 'properties' and look at the picture url when they right click.
Wishing Well: Set up a page for a wishing well activity. Not every member will get what they want, but a couple lucky people will. Make sure you remember to put in the price range members can choose items from. Different ranks can have different price ranges. For example, a lower rank would buy a 'ticket' for the wishing well in the donation shop for X amount of NP (all tickets the same price) and would be able to choose a prize from 2k-5k. A higher ranked member would be able to ask for a prize between 2k-10k. Remember to put limits on how many tickets they can buy.
Scavenger Hunt: These aren't very popular, but I think it's fun. :) Ask the members to get 'BLAH' items and turn them into 'USERNAME' and they will get something more than what they have paid for. Remember to check the pricing!
Mystery Pic: Guess the picture. When saving on server, make sure it has no clues as to what the picture is. It can't be to hard though!
'Caught'ya' advertising: Obivious. Whoever you catch advertising for your guild gets an item.
Banner making: Get your members to make banners for the guild. X amount of NP/ITEM for 1 banner OR the best banner gets X item/NP. Make rules such as, Neo-related ONLY or Anime ONLY. This can be done with a guild layout too.
Story Time: Members tell stories. Best story wins.
Contests are not allowed in neopets. The owner can be frozen. It is in the neopets rules. Activities are okay however. A contest is not allowed because it makes people spend a lot of NP and sometimes they do not get anything back in return. This another form of scamming, even if there are consolation prizes.