J.A.C.K. - General-purpose BSP tool aimed at all Quake-based engines. The free version runs on Windows and Linux. Currently the most stable of the modern Hammer clones. There's a paid Steam version that's slightly more up-to-date, and has Mac support. JACK is almost identical to Hammer, making it easy to use as a drop-in replacement, and tutorials for Hammer will make sense when using JACK.
TrenchBroom - A Quake editor that has support for Half-Life as well. Runs Windows, Linux, and Mac. Doesn't currently render sprites and models in the editor, but otherwise fully works for Half-Life mapping. A very stable application that is being updated often, but is very different to Hammer, which will make most tutorials difficult to follow. TrenchBroom has an excellent manual to assist with that, however.
Quark - The Quake Army Knife, another tool aimed at being a universal editor. Don't forget to install the required addons to enable mapping for your chosen HL mod.
GtkRadiant 1.4 or 1.5 - Half-Life has never been a big focus of the GtkRadiant project, and support for it has been removed in version 1.6.
Sledge Editor - A free, open-source replacement for the Hammer Editor that's no longer being actively developed. Unfinished and rather unstable - use with caution.
Game Data Files
In order to use an editor for more than empty rooms, you'll need a FGD! An FGD file contains the definitions of the entities in a game/mod so you can create a map for it.
Sven Co-op: Check your Steam installation, the FGD is included at /Steam/steamapps/common/Sven Co-op/svencoop/sven-coop.fgd
For non-Valve games and mods, consult the mod website. Often the FGD is included in the mod install folder.
Vluzacn's ZHLT v34 - The most up-to-date and feature rich version of the Half-Life compile tools, with a host of lighting options and optimization entities. Includes 32- and 64-bit builds, so you can get more power if you're running a modern system. Official home on the Sven Co-op forums.
Nem's Batch Compiler - An interface for the compile tools, if you don't like using the command line or compiling through your editor.
HLFix 0.81b - A tool that converts a Hammer RMF to MAP files. In the process, it performs a number of geometric operations to fix common problems with brush geometry. Some custom builds of Hammer include these fixes by default, and the modern Hammer alternatives do not require HLFix.
fixprt - Fixes VHLT v34 portal files, allowing you to import them into J.A.C.K.
To actually create texture images, use your favourite image editor such as Photoshop, GIMP, Paint.NET, etc.
WadMaker - A new tool that can turn a directory full of images into a wad file, or extract textures from wad and bsp files. Special support for water fog color, transparency and external image conversion tools. Official website
kHED (or older free version) - A basic - but easy to use - modelling tool to edit low poly models. Has good support for Half-Life.
MilkShape 3D - A popular (but non-free) model editor with good support for Half-Life. A 30 day trial is available.
Blender - A free, fully-featured modelling program that supports animations. Install the Blender Source Tools (which also support Goldsource) to get Half-Life support. A guide is available here.
Crowbar - A convenient app which allows you to easily compile and decompile GoldSource and Source models.
Ambient.Impact.Design - Ambient.Impact's old website has arguably the best HD character models made for Half-Life, it's expansions, and a couple mods, often with source files included for those inclined to make edits.
Half-Life SDK on GitHub - Official GitHub repository for the same code released in the SDK, but with additional updates and bugfixes.
Half-Life Updated - A version of the official Half-Life SDK, updated to support Visual Studio 2019 and fix many bugs. If you are starting a new Half-Life mod and don't plan on using Spirit (see below), it is strongly recommended you use this version of the SDK.
Half-Life SDK 2.3 - Though heavily outdated, this package encompasses everything Valve made available to the general public back in the day, including model and map example source files, early models and map compile tools, and full dll source for Half-Life and multiple official mods.
Spirit of Half-Life 1.5 (Or 1.8) - Laurie Cheer's mod that adds a whole mess of quality-of-life features for mod authors. Have buttons and breakable glass move with your elevator, give every NPC a unique model, or fill your map with particle effects. 1.5 and 1.8 are more or less the same feature-wise but each have their own set of minor bugs you'll have to fix on your own using the included source code.
Spirit of Half-Life Updated 1.8 - Spirit of Half-Life applied on top of the Half-Life Updated SDK, with support for VS2019 and Linux compiles. If you are starting a new Half-Life mod and want to base it on Spirit, it is strongly recommended that you use this version of the SDK. There are also branches for other versions of Spirit: 1.2, 1.4, 1.5, 1.8
Jed's HLMV - An updated version of the official Half-Life Model Viewer supporting all HL texture features.
Crafty Object Viewer - View models, materials, or even the geometry of compiled maps for both Source and Goldsource. Also supports exporting data to obj, if you need to use map data for creating animations or models.
GCFScape - Browser utility for opening now-deprecated Source GCF files to view or extract content. Also compatible with HL pak files, wads, bsp files with packed information, and Source VPK files, making it an essential tool.
Slackiller's Half-Life Programs - Slackiller hosts a bunch of tools that would otherwise have been lost over the years - including a lot of things linked on this page! Hammer builds, compilers, viewers, and miscellaneous utilities abound.
Valve Developer Union - Tool archival site dedicated to keeping Goldsource modding alive. If you can't find it on Slackiller's site, and it's still floating around, you'll almost certainly find it here.
GS HL Tools - TWHL user Stojke maintains this repository of useful Goldsource-related modding tools.