Yesterday I came across a leaked version of Half-Life 2 (called anon-hl2), and since I'm a real Half-Life freak I couldn't resist trying it. There are a few mods using these files, so legally it shouldn't be a problem downloading and playing the beta.
Before Valve released Half-life 2 they got hacked via a security hole in Microsoft Outlook and a working copy of HL2 got downloaded. It's often referred to as the "Russian" version or beta, since it was on occasion sold on disks over there.
I don't know how it works for other players, but on Windows 7 x64 it crashes instantly. The solution is to run it in compatibility mode with WinXP SP3, but even then it crashes sometimes. Although it only crashes on mapchange/mapload for me, it might work perfectly on other systems.
Enough about the bugs.. more about the content. What is the beta like, you might ask - well.. it's an early draft. For example; after getting the car and changing level, you will find a house that you can only enter via the basement. In HL2 it's destroyed internally, but in HL2 Beta it's intact. There are hundreds of changes in map design, as well as models and textures. The most interesting part is, however, the left-out weaponry and conversations.
Example, normally (at Eli's lab) Alyx states that Mossman talks about how she should've been in the test chamber that day. In Half-Life 2 Beta Eli tells you that it could have been Mossman. Some lines, i.e. "She's the reason to why I spend so much time outside" are preserved in the official release, but re-used in a different context.
I don't know what Valve's take on this is, but as previously mentioned there are mods using the files and I've read that it's okay to download and use as long as you're not pushing the limits. Gary's Mod is using some files from the beta (Phygun, mainly).