Yes, yes. Let's get the "HURR WINDOWS 8 SUX0R" and "lol but this game wasn't guaranteed to work on W8, #lrn2readfaget" or "I see your problem; you're running W8 and should downgrade" remarks out the way and put our big-boy pants on. Yes, yes, you're all very clever people and these remarks have literally never been said by anyone before and you're completely novel and witty.

The rest of the class will be reading on while you fiddle with your ego in the back...

Credit goes all the damn way to Jeff for making this possible. Seriously, throw your thanks at him for doing in three days what Vlambeer neglected to do for years.
A quick history lesson. This game is pretty terrible when it comes to post-W7 compatibility. You'd be lucky to play for more than five minutes before the game crashed. Sometime towards the end of 2013, Rami of Vlambeer said that the fix was fairly simple and would take a few weeks to roll out the fix. As of writing (Q2 2015), Vlambeer has been mum on this, ignoring all correspondence that confronts them on it.
I'm not going to use this guide to spread anti-Vlam sentiment. You're here for a fix to make this silly little timewaster of a game work.

First things first, you need an IPS file. This is basically a patch file. What does it do? Who knows. It makes the game work.
You can download it from this mirror[www.dropbox.com].

Backups are recommended, but SSTRE is small and doesn't work in this state, therefore it is just as easy to delete the game and redownload it.

1. Download the IPS .zip file.
   
2. Download the Lunar IPS Patcher[fusoya.eludevisibility.org]. Any competent IPS Patcher will do, but these instructions will cater to that particular one. CTRL+F for "Lunar IPS (WinZip File)" if you have trouble looking for it.
   
3. Install Lunar IPS. Duh.
   
4. Extract the IPS from the ZIP. Having installed LIPS, the icon should be of a pink heart. If it is not, stop and go to the next section.
   
5. Open the IPS file (double-click), and it will open a Windows File Open dialog.
   
6. Find the SSTRE folder. It will be at Steam\SteamApps\common\Serious Sam The Random Encounter (on the drive in which you installed this game). If you can't find it, go to The Random Encounter's Properties page in Steam and select Browse Local Files.
   
7. In the File name field, type sstre.exe. The dialog box should suggest it after the first few letters. Don't worry that it says "No items match your search".
   
8. Wait for the Patcher to finish (it only takes about 2 seconds).
   
9. Play!

Some computers like to be contrarian. This one is for yours. Follow the earlier instructions up to step 4 and then follow these instead.

1. Open Lunar IPS Patcher. It will open a window with few buttons. Select Apply IPS Patch.
   
2. It opens the Windows File Open dialog, asking for the file you'd like to use. Find the sstrcf.ips file you extracted earlier and select it.
   
3. The box will open again, asking for the file you'd wish to apply it to. Find the SSTRE folder. It will be at Steam\SteamApps\common\Serious Sam The Random Encounter (on the drive in which you installed this game). If you can't find it, go to The Random Encounter's Properties page in Steam and select Browse Local Files.
   
4. In the File name field, type sstre.exe. The dialog box should suggest it after the first few letters.
   
5. Wait for the Patcher to finish (it only takes about 2 seconds).
   
6. If the patcher is still open, close it.
   
7. Play!

This data is sourced from [Windows 8 Crash Fix] SS: The Random Crash Fix written (and programmed) by Jeff. This guide exists for those who, like I, would check the Guide Centre before wading through the Discussion Centre. Just to bring this full-circle, here is the readme penned by Jeff...

Początkowo opublikowane przez Jeff:

Serious Sam: The Random Crash Fix

This is a patch for the PC game Serious Sam: The Random Encounter (by Vlambeer) to fix crashes that occur on Windows 8 machines. This has not been fully tested yet, please report problems to the forum thread where you found this.

How to install -
0. (Optional, but recommended) Go to your "SteamApps\common\Serious Sam The Random Encounter" folder and create a copy of sstre.exe.
1. Extract the .zip folder that contains the sstrcf.ips file.
2. Download and extract Lunar ISP: http://fusoya.eludevisibility.org/lips/
3. Open Lunar ISP and click the "Apply IPS Patch" button.
4. Find and select sstrcf.ips. Click open.
5. At the bottom right of the window where it says "Most Common ROM Files", click that and select "All files (*.*)".
6. Go to your "SteamApps\common\Serious Sam The Random Encounter" folder and select your sstre.exe file. Click the Open button.
7. Click Ok and start the game up with steam.

Now go out and waste some Serious time. The comments box is open if clarification is required. Such clarification will be integrated into the guide afterwards.