Yes, you can install both operating systems on your computer. This is known as dual-booting. It's important to point out that only one operating system boots at a time, so when you turn on your computer, you make the choice of running Linux or Windows during that session. If you're interested in running Windows programs under Linux, you should see the section: Can I run applications for MS Windows on Linux?
If you're going to have this kind of a system, it's important that you install the Windows operating system first in the first partition of your hard disk. You can then install Linux and along with it a program known as a bootloader (nowadays, the most popular are LILO and GRUB) which allows you to choose your operating system. The Linux installation process, in most circumstances, leaves your Windows partition alone during the install. Installing Windows, however, will destroy the information left by bootloaders and so should never be installed second. Due to Microsoft's monopoly on operating systems, most computers have Windows on them before anyone contemplates installing Linux, so you may have to repartition your hard disk - that is, divide what may be a hard disk with only one large partition (known as C: in the Windows world) into two or more different partitions so that Linux can be installed and kept separate from Windows. Third party tools such as Partition Magic generally work well for this purpose. After the re-partitioning, you're free to install Linux.
Due to the increasing availability and reliability of virtualization technologies, there are also methods to run versions of Microsoft Windows in "virtual machines" inside Linux. One can also run versions of Linux inside Microsoft Windows.