For 12.04

^{Derived from Pavlos G. answer and inspiration from Darmien answer.}
Different version? Go to the list.
See the end of the post if you are in trouble and want to revert the changes.

1. Ignore the purchasable apps

Open a terminal (Ctrl + Alt + T) and type:

gksu gedit /usr/share/software-center/softwarecenter/db/update.py

And press Enter. You'll be prompted for your password.
Then an editor will appear. Locate the following lines (hint: Ctrl + F may help):

        doc = make_doc_from_parser(parser, cache)
        if not doc:
            LOG.debug("make_doc_from_parser() returned '%s', ignoring" % doc)
            return
        term_generator.set_document(doc)
        name = doc.get_data()

Immediately after those lines, paste the following (including the spaces!):

        if doc.get_value(XapianValues.PRICE) not in (""): return

Note: if you want to keep stuff that doesn't cost money, but has to be "purchased"
(like trials, magazines and other propietary stuff), replace ("") with ("0.00", "").

Save the file (Ctrl + S), open the Software Center and… voila!
There are no commercial programs!
You can close the editor and the terminal now.

2. Remove the "For purchase" channel (optional)

To also remove that "For purchase" item in the menu, open a terminal and type:

gksu gedit /usr/share/software-center/softwarecenter/backend/channel_impl/aptchannels.py

Locate these lines:

        if get_distro().PURCHASE_APP_URL:
            channels.append(for_purchase_channel)

And disable them by putting a # in front of every line:

        #if get_distro().PURCHASE_APP_URL:
        #    channels.append(for_purchase_channel)

Save and enjoy a software center without ads!

Side notes: The. files. are. packaged.

What does this mean, you ask? This means that,
whenever you upgrade your Software Center, the changes
will be reverted and you'll have to do this steps again.

Undo the modifications

If you want to restore the original state of the files,
open a terminal and type:

sudo apt-get install --reinstall software-center && exit

Again, you will be prompted for your password, this time on the terminal.
Type it and press ENTER. Don't worry if nothing appears when you type, it's to hide your password.
The terminal will automatically close when finished.

try to uninstall it from terminal

sudo apt-get autoremove (app name)

and about this problem try to search in software sources may be you put repository broken or something like that and remove it from other software tab in software sources

and try this command may help you

1. sudo apt-get check

2. sudo apt-get update

3. sudo apt-get upgrade

4. sudo apt-get autoclean

5. sudo apt-get purge

and restart afte that try again

if not you can do that but i'm sure the won't help you but try it remove ubuntu software center by this command in terminal

sudo apt-get autoremove software-center

and return install it

sudo apt-get install software-center