Jatinder Pal Singh

Version 2.2 Completely Re-Written. 
Tested with WordPress 4.1 and Buddypress 2.2.1. 
This plugin gives an option to buddypress based website owners to decide that where their users should be redirected after the login. Currently users can be redirected to 3 different locations after login. 
1. Personal Profile / Personal Activity Page 
2. Site wide Activity 
3. Friends’ Activity 
4. Custom URL
After Logout, Users will be redirected to Homepage. No Separate plugin required for this.

BP Login Redirect

Allows to decide buddypress website admins where their users should land after log in.

mort3n

This plugin lets you have a normal site Homepage for visitors while logged-in users have their BP Profile as Homepage. This is similar to Facebook. The redirection can be disabled for a particular role.
** When a user logs in, (s)he is redirected to the BP Profile.
** When a logged-in user goes to the site Homepage, (s)he is redirected to the BP Profile.
** When a user logs out, (s)he is redirected to the site Homepage.
The plugin is successfully tested with WordPress 3.6 and BuddyPress 1.8.1
Note: This plugin is a fork of the excellent plugin https://wordpress.org/extend/plugins/bp-profile-as-homepage/ by Jatinder Pal Singh. This fork updates and improves the code in a variety of ways.

BP Profile as Homepage Fork

This plugin lets you have a normal site Homepage for visitors while logged-in users have their BP Profile as Homepage. This is similar to Facebook.

BP Login Redirect vs BP Profile as Homepage Fork