Postal 2 is the king of games that aged better IMHO. It has received absolutely extensive patches since it came out especially in the last few years, as well a s a massive expansion pack, support for widescreen, high resolution, multi-monitor/eyefinity and countless other features. You can even take a piss on a copy of Postal 3 found in the junkyard in the game.
Half-life, Half-life 2 and most other Valve games. Valve still to this day supports these games and regularly updates them with patches every few months or so. They put out the source engine update of the original Halflife and there are countless other improvements over time. There's now a community made mod for Half-life 2 that is endorsed by Valve that improves the graphics of that game greatly as well and it's free for those that own the base game.
The Lord of the Rings: The Battle for Middle Earth II and it's expansion The Rise of the Witch King: The game carried on a life of its own in the community after EA stopped updating it, and there are community made patches that fix endless bugs in the game, add widescreen high resolution support, rebalance multiplayer and countless other benefits.
Command & Conquer: Again, fan made patches greatly improve the original game with high res support etc.
Baldur's Gate 1&2 and many of the other D&D games all have fan made patches/mods that add high res, widescreen, HUD scaling, combine the games together into one larger game using the newer game's game engine etc.
Tomb Raider 1 (and possibly some of the other TR games as well) has higher resolution support now due to features of DOSbox, glide wrappers and other hacks.
Blood: Supports widescreen/highres monitors also that never existed when the game was made or for many years after. I've ran this ancient game at 2560x1600 resolution. Crazy.
Most if not all ancient DOS games can potentially be played with a better graphical experience of either higher resolutions or via shader customizations in DOSbox configuration or via 3rd party utilities and addons to simulate old CRT displays and other customizations. Also, all of the games that irritating copy protection that involved looking things up in the manuals or using some obscure code wheels, cards or other crap that came in the game packaging is all disabled and DRM-free now eliminating those frustrations from the past to let the gamer enjoy the damn game without such irritations. :)
As an extension of the last paragraph for games on GOG, any that did have DRM don't have it now, so that's an improvement over the originals that will have varying degrees of improved user experience depending on how much of a PITA the DRM on the originals were.
Most if not all games also can now be enjoyed more by having a wide array of input hardware that either didn't exist before or which is much more advanced and capable now than hardware from the past. For example, the original Star Wars X-Wing games had mediocre input device support compared to what we have today. Some of them did not support a throttle IIRC, but with modern flight controller hardware, you can program the hardware's drivers via a systray applet or similar to simulate the keyboard/mouse/joysticks so you can make your various buttons and gizmos on the fancy hardware convert their input to something these ancient games can understand. Same thing with other programmable mice and keyboards like my Logitech G600 20 button mouse for example. I'd have killed to have something like that to play ancient games like DOOM/Quake or just about any old games back then.
Our computers are insanely fast and infinitely capable too, so all the old games can not only be played, but they can be played in the highest resolution they support with all fancy graphics or other options enabled to experience them in their absolute best way possible, whereas when they first came out we might not have had hardware that could experience the game at the maximum settings etc.
All of these things will improve games, but then that's offset to some degree by how much fun the actual game engines, storylines, gameplay and other factors of a given game are to us now too. I have a blast playing ancient games on modern harware with modern input devices on a 30" screen with everything maxed out. It's awesome sauce. The past meets the future. ;)