Most 3D games make use of it. The latter two Panzer Dragoon games use it (although disable either button X or Z for Zwei, because somehow it gets triggered when you hit the R button and you could pop your Berserk unintentionally). Daytona USA interprets it as a steering wheel, for whatever reason, but I think it enables analog turning (not entirely sure about that). Croc has pseudo-analog control, surprisingly for a tank-controls-based game, if you want to try it. Burning Rangers definitely uses it.
Specifically, there are three different analog controllers for the Saturn. Around launch, Sega released two, the Arcade Racer wheel, and the Mission Stick joystick. Later, in fall '96, they released a third, the 3D Controller. This is a little bit like the PS1, with its twin joystick, neGcon, and dualshock, but there's a difference -- the three analog controllers on the PS1 are all incompatible, while the three on the Saturn are all partially inter-compatible.
That is, many games that were designed for the wheel also have analog on the Mission Stick and 3D Controller. Some games designed for the Mission Stick also have analog on the 3D Controller as well. There are some games that require each one of the three for analog -- games designed for the 3D Controller only, released after its release along with NiGHTS, won't work with the other two (apart from racing games, which also work with the wheel because they were designed to support it), first. Second, while most racing games designed just for the wheel work with the other analog controllers (Sega Rally and Daytona USA (first version) both work with all three, for instance, with the latter two imitating a wheel), there are a few, most notably Virtua Racing and Hang-On GP, that require the wheel for analog. These games are a lot more fun with the wheel than with dpads. Some later, post-3D Controller, racing games don't work correctly with the Mission Stick, too, such as Daytona CE. That has native 3D Controller support, though, which is good. And third, while most Mission Stick games also support the 3D Controller (and note, there are a lot more games that support the Mission Stick than you'd realize by just looking at the miniscule number of games with its logo on their box. Most games that were designed for it, such as Panzer Dragoon, PD Zwei, MechWarrior 2, etc., don't have Mission Stick logos and don't mention it in their manuals, in the US/EU versions at least.).
The two (Mission Stick and 3D Controller) are different, though, so this leads to some control differences in games designed for the Mission Stick when you play them on a 3D Controller -- the Mission Stick is much more precise, of course, and has a square gate, while the 3D Controller has a round gate and isn't as precise (being just a gamepad). This matters in the first Panzer Dragoon, because when you play it with a 3D Controller, you can't shoot at the corners of the screen -- the game has you fire at the part of the screen you're pointing at, as if the Mission Stick's range is the screen, so because of the different gates, you can't shoot at the corners with the 3D Controller. Zwei changes its controls, so that issue doesn't happen there, but that game has its own unique feature -- it actually has a twinstick mode, where you aim with one stick and fire with the other. To use it, you need two Mission Sticks. Then, remove the stick portion from the second stick, attach it to the first one (you can attach two sticks to one Mission Stick base), and plug the second one's stick into the "Sub Control" port on the bottom of the base. This is the only game I know of that supports this twinstick Mission Stick mode, oddly enough.
However, most all 2D games don't use it, so you're just as well off using the standard 2D pad for those titles.
No, the 3D Controller has a great dpad. You can use it for everything, it's the only Saturn gamepad I use. Just switch the switch over to digital mode for games that don't support analog.
You seriously don't get better than this. Also, the Japanese sequel ... Dynamite Cop 2 or whatever it was called. Awesome games.
The first game is "Dynamite Deka" in Japan (for Arcade/Saturn), and the second is "Dynamite Deka 2" (for Arcade/Dreamcast). In the US, the the platforms and games are the same, but the names are changed -- the first one is "Die Hard Arcade", and the second is "Dynamite Cop". And yeah, they're fun games for sure. I do think the second one's better, though; the first is completely linear, so it's the same every time, and doesn't support saving either on the Saturn (seriously, forcing you to play that tedious sub arcade game every time in order to get more credits isn't a great design choice). Dynamite Cop has multiple routes, and you make choices along the way, so it's a more varied game. I actually like Sega's next (and last?) beat 'em up, Zombie Revenge for the DC, better than either of them though... but yeah, they are fun.