Good Old Games
GoodOldGames (gog.com) is a great site. The guys behind this site aim to bring back the old games you loved with an easy to use site, which allows to you download and run pre-packaged games which ensure that they run on your current operating system.
While some games will run natively despite their ages, Good Old Games have tested and created packages that ensure the game will run with minimal fuss while maintain the original experince of the game. Some games have been pre-packaged in a DOSBox (emulation software) meaning they have done the hard work for you so you can get straight to the game.
The account system means that you buy once, download anytime. This also means that you can download the PC and MAC versions as need (as they're available).
If you're looking for the easier way to play the classics, this is my first stop.
Steam
As you probably already have seen, Steam has a large array of game downloads including the classics. As any other Steam game, this is added against your account and can be downloaded at any point.Most classic games here are as they are. Another great resource for classic games,
DOSBox
DOSBox is a x86 emulator that allows you to install and run any DOS-based application in an emulated, sandboxed environment. This means that if you already have your classic games, you can install them to your DOSBox and get playing with minimal fuss.
DOSBox is available on almost all platforms (Windows, Mac, Linux, BSD etc) with custom frontends, and language translations available.
Virtual Machines
The last option which I can offer is to setup a virtual machine. This will require a bit more leg work on your side, but this will also give you the most genuine experience (without setting up old computer hardware).
Virtual Machine is a virtual computer running on a existing system. This means you and install and run any operating system, on top of an existing system without interaction.
Using the open source software VirtualBox (no relation to DOSBox) allows to create virtual machines with a wide range of supported operating systems from Windows and Linux. Simply setup a DOS or Windows 9x virtual machine and install your game.
Note: You will need the operating system media and product key to setup a virtual machine.
