Here are some useful applications from the Google Apps Marketplace that have a free version and you can consider them installing to your Google Apps account.

1. ManyMoon – This is an online project management software that is free and will integrate with Google Calendar as well as your Google Docs storage.

2. Aviary – This like adding a stripped version of Photoshop to your Google Apps. With Aviary, you can not only created and edit photos online but the app also has an audio editor for recording / editing podcasts and music. Aviary will save your file into a designated Google Docs folder.

3. Offisync – With Offisync, you can edit Google Documents right inside your Microsoft Office programs. It can also save documents from the desktop to your online account right within Office.

4. Zoho Projects – This is a more mature web-based project management app for Google Apps that also includes a wiki. Its a premium app but you can create one project for free – see more project management apps.

5. Google Short Links – If you don’t want to use bit.ly or tinyurl.com for shortening URLs, use the Short Links app from Google. It lets you setup your own redirection service on your personal Google Apps domain.

6. Spanning Backup – If you ever wish to backup your Google data (like documents, calendar and contacts) to the cloud, this app will come handy.

7. Time Report – This will add timesheet related features to Google Calendar so you track the time spent on various activities.

8. SlideRocket – Not happy with the presentations module of Google Docs? Try SlideRocket, this is one of the best online presentation apps on the Internet today.

9. Mail Chimp – Gmail has a strict daily sending limit so if you want to send bulk emails from Gmail account, use MailChimp – the service is free for lists up to 500 emails.

10. Survey Monkey – You can use the build-in Google Docs for Surveys but it you want something more personalized and customizable, try Survey Monkey – the basic version is free.

Finally, I’ll leave you with this creative video from Box.net that demonstrates how their service integrates with Google Apps.