Space Gun

It was obvious that Taito was inspired by Alien while making this. Also, they were one of the few third-party developers for the system who made quality stuff.

Rampart

Port of one of my favorite Atari arcade games, though I have it on Midway Arcade Treasures. By the way, Tengen was the console-publishing division for Atari Games, inc. In addition, Atari was split into three separate companies when the Video Game Crash hit.

Super Space Invaders

This needs no further explanation.

Cloud Master/Chuuka Taisen

Hot B did a great job at porting this game, and this is one of the rare few titles that had FM chip support. (Only the JP version of the SMS had this.)

Darius 2/Sagaia

Possibly the only Master System game that had parallax scrolling.

As an added bonus, here's a PSG rendition of Captain NEO from the first Darius:

Update: Here's more non-Sega ports that I missed:

R-Type

This was obvious, but it just had to be included. Plus, Irem also added an extra level to this.

Rastan Saga

Another Taito arcade port, but it's still good though they had to change a lot of things while doing so.

Captain Silver

Based off of one of Data East's worse games, Sega took it and made it much better.

Forgotten Worlds

Nothing more needs to be said

Strider

Unlike the last game and the next one, this port felt like an afterthought.

MERCS

I apologize in advance for choosing a video with audio commentary.

Ghouls 'n Ghosts

This port had the most changes when compared with the previous three.

Renegade

One of the two Technos titles that were brought to the SMS.

Double Dragon

And here's the other. However, II and III weren't ported to the SMS.

Vigilante

The other Irem port for the SMS.