Do I need to reinstall OS after macbook upgrade? My MBP mid-2009 is starting to slowly fall apart, so I figured I need a new one. I got an SSD for my current macbook, which has OS and apps installed, etc. 

Can I just insert this system disk into a new macbook and boot from it? What are possible issues (with Windows I'd worry about drivers)? 

Or do I need a migration process of some sort?

I am on latest Lion and I use Time Machine, if it matters.
This might help:

Does restoring from Time Machine also restore installed applications?

When you boot up on a fresh install you can run the OS X migration process to restore from Time Machine.

Unlike Windows you should be fine just restarting from the system disk though. All the necessary drivers are built in.

If your new disk has stuff on it, you can boot from it and run Migration Assistant from Utilities to copy your user directory from Time Machine.

Also, you should clarify, are you adding an SSD (e.g. into the optical slot) or are you replacing the existing drive? If you're replacing it you'll need a way to copy the data, i.e. from Time Machine.