Stargunner (1996) and Raptor: Call of the Shadows (1994): If you’ve played Strikers 1945, Tyrian, Gradius, or other scrolling plane shooters (Yes, I know some of those examples are vertical-scroll while others are horizontal-scroll), you’ll be right at home with these. Stargunner and Raptor both put you in control of a sci-fi jet fighter, facing off against waves of enemies and usually ending the level with a large boss. The major difference from most games in this genre is that you accumulated money between stages, and could spend it on various upgrades. New engines, energy shields, different weapons, and so on. They allowed a lot of personalization as a result, and definitely contributed to this genre’s history.

Stargunner is available as legal freeware, while Raptor remains shareware even today. Do note that Raptor reportedly has control issues with its Windows-native version, so you may want the DOS download anyway, which is what 3D Realms provides. These games can be obtained at:

Stargunner: http://www.3drealms.com/stargunner/
Raptor: http://www.3drealms.com/raptor/

Commander Keen series:A series of platformers in a different vein than Duke Nukem, the Commander Keen series was much more light-hearted and placed an emphasis on both exploration and tricky long-range jumps. This was because Commander Keen was a young boy fighting very cartoon-style aliens, armed with a cheesy 50s style ray gun, and a pogo stick for getting around. While the graphics for most of the games in this series frankly look laughable today, they all play pretty well and remain very fun. You have two options here; you can run the games via DOSBox, or CloneKeen; the latter is a remake of the Keen engine to run on modern systems, and there are ports for several systems... including the Wii if yours is homebrew-capable. Most of these games remain shareware.
Some of the games, and CloneKeen, can be obtained at:

Commander Keen 1: http://www.3drealms.com/keen1/
Commander Keen 4: http://www.3drealms.com/keen4/
CloneKeen: http://clonekeen.sourceforge.net/
CloneKeenPlus: http://clonekeenplus.sourceforge.net/