A list of all official patches can be found here.
A huge patch, it adds support for modern Windows, extra renders, multiple bug fixes, and many other additions. It also includes a patch to allow Unreal to run natively on Linux.
It can be found here.
If on Mac, try Unreal Gold OS X instead.
Fusion Map Pack - Adds 6 multiplayer maps to the game and is the only official bonus content for Unreal.
The vast majority of graphical tweaks are accomplished by editing the game's .ini configuration files.
With 'Unreal gold' Steam version edit <path-to-game>/System/Unreal.ini. To obtain 1920x1080 replace the current values for x/y.
Installing the Direct3D 10 renderer allows you to play the game in high-resolution, widescreen, and Direct3D 10. There's also a Direct3D 11 renderer, but currently no significant changes from D3D10 renderer. It is also worth noting that the DX10/11 renderer will not work with the 227 Old Unreal Patches.
Replace the original textures with S3TC Textures and get amazing detail. Do not use these server-side.
Replace the original skins with lore faithful High Resolution Skins
Various modifications, custom content such as characters, maps, plugins, and total-conversion mods can be downloaded and installed for Unreal. Like every game in the Unreal franchise, there's a ton of mods floating around the web on fansites like Oldunreal.
Maps are custom levels that are created using mod tools or editors.