Short answer is yes. To be frank it depends upon the application. Popular Windows application can be run using Wine software under Linux (and UNIX like oses). Wine project aims to allow a PC running a Unix/Linux like operating system and the X Window System to execute x86 programs for Microsoft Windows.
Wine can run many popular windows application such as MS-Office, Dreamweaver, Internet Explorer 5.5+, Adobe Photoshop 7, Illustrator 9, Acrobat Reader etc. See complete list of supported applications.
CrossOver Office is a commercial program of Wine software that allows many Windows-based applications to run on Linux. The actively-supported applications include Microsoft Office 2003, XP, 2000 and 97, Microsoft Internet Explorer 6, Macromedia Dreamweaver MX, Macromedia Flash MX, Adobe Photoshop, Lotus Notes and Quicken. A full list of application is available from CodeWeavers web site.
Other choice is to use VMware software on top of Linux, which allows to install Windows (and other operating systems) and its application inside virtual machine. VMware Workstation is one of the commercial software products sold by VMware Inc. The Workstation software consists of a virtual machine suite for Intel x86-compatible computers, which allows the creation and execution of multiple x86 virtual computers simultaneously.