There are couple of blog posts out there that talk about how to change passwords for SharePoint 2010 manages service accounts. You can do it using the GUI (Central Admin) or powershell.
I actually had to go through this exercise recently, and what I found is that certain service applications will stop working after the passwords have been updated. Specifically, the user profile synhronization service stops, and the search service application enters paused state.
After you change the passwords, you should probably check and make sure the underlying services are running. The two Forefront Identity Management services on which UPS depends will be stopped. Don’t try to start them manually, instead do it through Central Administration > Manage Services on Servers. You will be prompted to re-enter the password for your farm account.
Additionally, you may need to update the password for SharePoint Server Search 14 service. In my case it was straightforward, I rebooted my index server and the service was stopped complaining of logon failure. I just updated the credentials in services.msc snap-in and started the service manually.
There is one more step to get search working again, and that is to resume the search service application from powershell.
Run get-spserviceapplication, this will give you list of all service app IDs.
Copy the ID for your search service app and then run:
resume-spenterprisesearchserviceapplication -identity <search_service_app_id>.
This will resume the service app, and your scheduled crawls will start running again.
