The other day, I left a post about how to use DOSBox. But why use it when we don't have any of those old games? I can point you to some sites where it's possible to get games considered abandonware or freeware.
Besides that allow me to introduce to some the wonderful site that is Good Old Games (GoG to friends). This site was created a few years ago, with the idea to create free DRM games based on older titles. The is the main particularity of this site. You can buy old titles, like Settlers 2, any Ultima game, any old Might and Magic game, or others, for a fraction of price, and with the advantage that this games come ready to play on your current system (all thanks to DOSBox for many games). They also sell recent indie games (some of which are really good, Legend of Grimrock for instance). For the time being they have nearly 500 games on the list, and I bet some of these games will make you smile. Also, when you create an account, you will be entitled to 10 free games like Beneath a Steel Sky or Ultima 4, so there is no loss of just go there and create an account. Besides that, every week they do some sales over some games, so it's not uncommon to see the game you really want, for half the price. This site been on my favorite list since almost I know it, and everyday I like it even more.
About Abandonware Well personally I only follow a couple of them, but I can name one or two that should be OK to use. One is Abandonware Ring. It's an group of sites that are devoted on supporting and distributing Abandonware. You can find there a long list of available sites that host some abandonware games.
Another site, and this one I use it much longer the the above mentioned, is Home of the Underdogs. It hosts a kinda big list of abandoware games. You can find games there like Al-Qadim: Genie's Curse, Albion or Alien Legacy, to name very few of the possibles games found there. These games, you will need to use DOSBox, and will have to configure it manually. Just read my previous post.
These Abandoware sites, are the best option you can get to get those old titles. Just be sure, you don't end up on some site that also boast warez. Abandoware Ring will point you to safe sites.
In another news, I'm currently playing on 2 games i got from GoG. Total Annihilation Kingdoms (medieval version of Total Annihilation) and Divine Divinity, a game that i always wanted to play and never got a chance. I will post something about these games soon.