Here are some of the best web based task management apps for teams.  The list is still in progress so stay tuned for new additions.

Product Summary Pricing
Trello Kanban style storyboard of tasks with To do, Doing, Done etc. Visually impressive with collaborative and activity listing functions Free, $8.33 per month for larger file attachments, additional integration options with web apps, improved organisation of projects
HiTask Simple, clear interface and the ability to share task lists across team members, File sharing, integration with Google calendar and email and reporting functionality. Full review of HiTask. Free, $192 per year for 5 licenses. Sliding scale for larger teams.
Producteev Web based project management for teams. Task chat, file attachment, activity notifications and mobile apps. MS outlook integration possible. Full review of producteev Free, $99 per month for enterprise bringing MS integration and support.
Flow Kanban style task management with team chat. Mobile functionality across IOS and Android platforms. Free for 15 days, $19 per month for up to 3 people. Sliding scale for larger teams
Droptask Visually impressive and visually oriented task management web app where traditional lists are accompanied by circles denoting projects and smaller interior circles the associated tasks. Comprehensive integration with other web apps, gmail, Dropbox, Evernote etc. Multi-platform and even offline working. To get many of the good functions though, payment seems to be a must. Free, $250 per year for 5 users with unlimited attachments/subtasks, improved task functionality (dependencies, emailing, reminders etc) integration with other online apps).
Asana Collaborative, web based task management. Project capabilities, task based chat, dashboards, file attachments, mobile integration. Free, $8.33 per user per month for unlimited tasls/projects, data export, improved administration
Workfront Farily comprehensive web based system spanning project management with Gentt functionality, resource and capacity management, resource levelling, even burndown charts, document management and task based communication Pricing on request, $360 per year for work licenses, $720 per year for team leaders for plan licenses
Podio Kanban style team task management. Integration with many online apps (Evernote, Google calendar, Drobbox etc.) file sharing and mobile integration $9 for basic, $14 for plus and $24 for premium per employee per month. Upgrading between the plans enables unlimited workflows and visual reporting.
Zoho More focussed on project management than many other web apps here. Gentt functionality, multi-level subtasks, time sheets, document control for projects, reporting, task notifications and integration with Google apps Free for 1 project, $20 per months for 20 projects, $40 for 50 projects