The thing that Basecamp does well is that it is a generic project management tool that can be used for any kind of project - thus its wide appeal. The most interesting alternatives are ones that specialize in particular types of projects. For example, if you are a designer there is Solo and if you are a product manager there is my product Aha! - http://www.aha.io. These alternatives specialize by taking the common elements of project management software (like todo lists, calendars and comments) and tailoring them towards a particular job function.