I recently switched back to using regular Basecamp for Lemon Productions projects. I tried many other services and tools but nothing else worked as well as Basecamp. 37signals did a redesign of Basecamp last year and it's really great - and fast. Unbelievably fast and smooth for being a web app.
Today 37signals announced Basecamp Personal that looks like a great option for small groups (5 people or less) to plan and organize events or projects.
You can see how it compares to regular Basecamp but the best part is that it's a single $25 fee to set up a project. No monthly costs or recurring fees.
My only issue with the limitations of Basecamp Personal is the user limit. A one-off, short-term project won't necessarily be limited to 5 people. You might need a group (i.e. a volleyball team fundraising for a trip) of people involved who won't all need to have active accounts, but at least be able to check in on what's going on. I guess for those scenarios 37signals would tell you to set up a regular Basecamp account - starting at $20/month - and then just cancel when you're done.
At present they're only opening it up to current Basecamp customers but you don't have to be an owner of a Basecamp account, just a user on someone's project. So if you're interested in trying it out and don't have a 37signals ID, leave me a note in the comments and I can invite you to a project so you can check it out.