Running Classic applications in Mavericks?

No

That's if by System 7 you mean a program from the early 1990s, late 1980s.

The similarly named Mac OS X 10.7 is not "Classic", but is an operating system that was current from July 10, 2011 to July 25, 2012. Those will for the most part run in Mavericks. To determine which ones will go to http://www.roaringapps.com/

The similarly named iOS 7 Apps will not run in any version of Mac OS X. iOS is the operating system designed for iPads, iPod Touch, iPhone, and AppleTV. Although data will sync with Mavericks from iOS devices. That isn't named Classic either. So make sure you are clear about what you are asking about.

Mac OS 9 applications will work on Macs up through 2005, if they have Mac OS X 10.4.11 or earlier installed with the Classic environment. Some Mac OS 9 applications will work within PowerPC Mac OS X up to Mac OS X 10.6.8 thanks to something called Rosetta. They have to be specially written in Carbon. Appleworks was one such program. Those will run in virtualization under 10.6 Server in Mavericks.

If uncertain what you are talking about, state the program name.

Yes, which program are you attempting to run?

PowerPC Macs running up to Tiger 10.4 had the Classic Environment to run these programs.

For Intel Macs, here is some information I compiled for another similar post:

With the newer Intel Macs, you have to run a Classic emulator such as SheepShaver, which requires you to extract the Mac ROMs from your older Classic Mac and then install Mac OS 9.

A related program is Chubby Bunny, which comes bundled with all of that included (google the term "Classic-On-Intel v 4.0.1 chubby bunny").

More information on SheepShaver:

http://www.emaculation.com/doku.php/sheepshaver_mac_os_x_setup

and

http://www.everymac.com/mac-answers/mac-os-9-classic-support-faq/run-macos-9-on- intel-macs.html

and more information about Chubby Bunny:

http://www.macwindows.com/OS9_on_Intel_Mac.html#092408b

and

http://hackthemac.blogspot.co.uk/2008/08/chubby-bunny-old-virtual-machine.html

Here is the Classic CD-ROM version of RISK II running in SheepShaver on my Lion Mac:

[click on image to enlarge]

The legality of doing this is questionable. The ROM from what I understand is subject to copyright. Extracting the ROMs or being part of the distribution system may violate DMCA. I'm no lawyer, but this forum does say to post within the law.

The legality of most things like this can change with jurisdiction.

There are many other SheepShave posts here:

https://encrypted.google.com/search?sitesearch=apple.com&q=sheepshaver&as_qdr=al l&newwindow=1&num=100&filter=0

...and US Copyright Law respects "fair use."

These ROMs were manufactured well before the DMCA.

i Could Never Get SheepShaver To Work. 😠

Really? Worked for this guy:

https://discussions.apple.com/thread/5804036?answerId=24565363022#24565363022&ac_cid=tw123456#24565363

Here is a recent post I assembled about SheepShaver and Chubby Bunny:

Here is a recent post I assembled for these:

With the newer Intel Macs, you have to run a Classic emulator such as SheepShaver, which requires you to extract the Mac ROMs from your older Classic Mac and then install Mac OS 9.

A related program is Chubby Bunny, which comes bundled with all of that included (google the term "Classic-On-Intel v 4.0.1 chubby bunny").

More information on SheepShaver:

http://www.emaculation.com/doku.php/sheepshaver_mac_os_x_setup

and

http://www.everymac.com/mac-answers/mac-os-9-classic-support-faq/run-macos-9-on- intel-macs.html

and more information about Chubby Bunny:

http://www.macwindows.com/OS9_on_Intel_Mac.html#092408b

and

http://hackthemac.blogspot.co.uk/2008/08/chubby-bunny-old-virtual-machine.html

Here is the Classic CD-ROM version of RISK II running in SheepShaver on my Lion Mac:

[click on image to enlarge]