I will be a contrarian here and tell you that 37Signals may be a great company, but their product is only fit for either extremely unstructured companies or those under 5 employees.
As we have gone past 5 employees, we could not wait to get the heck out of every one of their tools we were using. And it was an absolute hell to move from so loosey goosey done "structure" they have to something a lot more disciplined.
BTW, Highrise is a very dirty word in our office. Spend the money on CRM for gorwnups, like SugarCRM, Salesforce, or Netsuite.
I use basecamp with two of my suppliers. The fundamental difference between basecamp and google apps is that basecamp is built for collaboration only, and it's useful for exchanging files. It works well for a limited amount of tasks: ToDo lists; discussion threads, uploading and commenting on files. I use it to share out wireframes, exchange files with the supplier and discuss current work. It's simple, so it's not a project manager, bug tracker or anything like that. It's good for what it is. You sort of learn to work within its constraints, and it's good at the limited set of features it has. My complaint about it is the search functionality is weak.
I'll admit that I've never got Basecamp. I've used it a few times, and always been surprised by how scrawny it is - no half decent search, zero usable process support and no sensible way of integrating other tools that fill the gaps. I like a lot about the 37signals stance in general, but this is a tool that survives (in my view) on reputation alone. It was a breath of fresh air when it was new, because it eliminated complexity that didn't add value. But everyone gets that now, so that's really no longer a point of advantage.
There are a few me-too services you can look at, as well as broader systems (such as Google Apps) that aren't really like-for-like alternatives but are fully credible. I'd suggest you break the question into:
Answering those will give you a pointer as to whether you need specialist tools, whether there's already a good default tool or set of tools, and where you need to prioritize.
Basecamp and other 37signals tools are really great. Though, in distributed teams you have to remember that just tools would not do all the work. You have to make sure that communication is good, team members know and understand each other well. For that, I suggest to use tools like Skype and Yammer to build up your communcation channels between the members. Also following each others Facebook and Twitter feeds often helps to build better relationships.
We have a distributed team with 9 people. I find some of the other comments mystifying about how you can't use 37signals beyond 5 people or with distributed teams. After all, 37signals itself has 20-some people and a distributed workforce. I am also mystified that someone would assert that an industry leader like 37signals is "surviving" on reputation alone. Oh please let me survive like 37signals!
That being said, we use both 37signals and Google Apps. I positively love Basecamp. I didn't use to love Backpack but it has grown on me. We use Pages, Campfire, Journal, and Newsroom all very effectively. We don't have a great need for a CRM in our company so I won't tell you Highrise is wonderful. I have great respect for SugarCRM and even Salesforce (if you can afford it).
The only thing we use Google Apps for is shared spreadsheets. But for that purpose there is nothing like it for the price.
Not sure where the disdain for 37signals comes from as my team uses Basecamp and Highrise every day.
I've tried MS Project and amalgamations of several others, but nothing is as clean and easy to use as Basecamp.
As for a CRM, Highrise gets my vote, hands down. I'd been a paying customer of Salesforce and I've tried Sugar. Zolo even has one I think I've tried, but nothing is as good as Highrise. For me it is the simplicity of having everything I need and nothing I don't...well, nearly everything I need. For those issues where it doesn't do exactly what I want, I have found their support to be exceptional.
I even went to far as to design a plugin to ping their API to get information out of my account that their off the shelf systemt did not provide and their development team was also super cool.
The function that was missing from Highrise was the ability to search for contacts that did not have a task associated with them. I knew there were a few in there, collecting dust, with no reminder to me to reconnect with them. So I created a plugin to access all of my contacts and dump those that did not have a task associated with them into an excel spreadsheet for me to follow up with in the future.
It's now available for free to all Highrise users - https://highrise.businessframe.com In any event, I really appreciate their attention to me as their customer, their pricing, cross platform integration, and generally the way they run their business. It's something I aspire to emulate.