- LDAP Client - query an LDAP Address Book and add contacts to your Android Address Book
- CardDav-Sync - synchronize your contacts with a CardDav compliant server (eg Zimbra); free and paid versions available.
- AnDal Calendar Sync - synchronize you Calendar with a Caldav compliant server (eg Zimbra)
- K-9 Mail - open source IMAP client that is better than the default email apps
- OpenDocument Reader - it does what the name suggests
- Opera Mobile - better than the default Android Browser
- Connect Bot - local shell and ssh client
- Nexus torch - simple flash light application that doesn't require permissions that make you wonder...
One handy service that I find not to be working right is delicious.com. After trying several applications none of those seemed to be working well and using the website directly is just not fast enough. Update: DeliciousDroid works great. Search Google Play for "deliciousdroid" (no spaces) or you won't find it!
If you are aware of other productivity-enhancing applications that don't require weird permissions please share in the comments section.