May I remove Python.framework in $PATH enviroment variable? I recently upgraded Python (via downloaded .dmg files). Before, my $PATH looked like this:

/usr/local/bin
/usr/bin
/bin
/usr/sbin
/sbin


Now when I run the command: 

$ echo $PATH | tr ':' '\n'


the following two lines are added:

/Library/Frameworks/Python.framework/Versions/2.7/bin
/Library/Frameworks/Python.framework/Versions/3.4/bin


I've noticed that my ~/.bash_profile has only the following content:

# Setting PATH for Python 3.4
# The orginal version is saved in .bash_profile.pysave
PATH="/Library/Frameworks/Python.framework/Versions/3.4/bin:${PATH}"
export PATH

# Setting PATH for Python 2.7
# The orginal version is saved in .bash_profile.pysave
PATH="/Library/Frameworks/Python.framework/Versions/2.7/bin:${PATH}"
export PATH


So, if the original versions are saved in their respective, python-specific .bash profiles, can I delete this content from my ~/.bash_profile?

Why would these duplicates be added to ~/.bash_profile in the first place?
Unless the new items are causing trouble, I suggest leaving them as-is. Most apps will probably have their desired version of Python bundled with them, but some may not, and some may want the 2.7 framework rather than the 3.4 version. The only issue I can think of is if Python 3.4 is running and accidentally stumbles over the 2.7 files first because they are first in the PATH.

As for where they're coming from, they're coming from your .bash_profile. The lines you pasted from there show the two directories being prepended to the PATH environment variable. Since they don't get added twice, the Python installation edited your .bash_profile directly. Removing them will, no doubt, remove them from PATH, with questionable benefit.

Finally, I would not recommend uninstalling both versions of Python. Keep at least the one that came with your OS. You might have some better control using MacPorts to install updated versions of Python, if you really need them. Again, you don't say if there's any real problem other than things looking funny, so it's hard to make recommendations.