Not all programs that could run in Windows 98 will run in Windows 7 or even Windows 8. This is in part due to the nature of the environment: Windows 98 was exclusively a 32-bit OS that could run 16-bit or 32-bit software, and Windows 7 and 8 are both available as 32- and 64-bit operating systems. Guess what, they can run only 32-bit and 64-bit software. If the program you want to run is a 16-bit app, you may be out of luck. And it is also more difficult to run a Windows 98 program in 64-bit Windows 7 or -8.
To check if you're running 32- or 64-bit Windows, in Windows 7, click Start, right-click Computer, and select Properties. (In Windows 8 it's Search, type system, click Settings, then System. Look for the System type field. Below we've solved this problem for Windows 7, but the principle is in essence the same.
Run Windows 98 programs in 32-bit Windows 7
Right-click the .exe file of the program you want to run, and choose Properties. Now click the Compatibility tab and ensure 'Run this program in compatibility mode for' is selected. Now choose and select the operating system you think best, we presume Windows 98. Try to launch the program, if it doesn't work first time going back through the process and selecting a different compatibility mode OS may work.
Run Windows 98 programs in 64-bit Windows 7
This is a little more difficult if you are using a 64-bit OS, as you need to virtualise a 32-bit environment. If you have Windows 7 Professional, Enterprise, or Ultimate, download and install Microsoft's free Windows XP Mode and Windows Virtual PC. This runs a copy of XP in a 32-bit virtual machine. You can then carry out the procedure outlined above.
Users of 64-bit versions of Vista, Windows 8, or Windows 7 Home can't do this. Now it gets complicated and expensive. In essence you need to download and install a free virtual machine program, such as VMWare Player. The trouble is you will need a licence for an older version of Windows such as Windows XP, to run on your virtual machine. Once you have a 32-bit Windows instance, you can then go through the steps outlined above. But you may simply decide to give up on your Windows 98 software (and I couldn't blame you).