Most of these are free, or at least offer trial versions, and many require no programming experience. Try a few of them before settling on one.

Adventure games

3D Adventure Studio – Create basic adventure games similar to Gabriel Knight 3. If you’re unfamiliar with the Gabriel Knight series, send GR editor Charlie Barratt a PM and he’ll regale you with stories about the greatest adventure game series ever.
Adventure Builder – A basic DOS/WIN text adventure creator.
Adventure Game Engine – A nice adventure game engine for creating first-person adventure games in the style of Myst.
Adventure Game Studio – Another quality point-and-click adventure game creator.
Adventure Maker – The most notable feature of this toolkit is its ability to create games for the PSP and iPhone. The full set of features will cost you $69 ($139 for commercial use).
ADePT – A fairly old adventure game designer.
ALAN – A neat little program for creating interactive fiction.
Aiee! – A simple interface for designing and playing text adventures.
M.u.C.e.S – The Multichoice Creation System essentially allows for the creation of interactive fiction in which the player chooses actions from a list. Ironically, the system appears to have been made in GameMaker, making it a meta game creator of sorts. It mostly works, but crashes occasionally.
Wintermute Engine – A very feature rich graphical adventure game creator.
ADRIFT – A simple interactive fiction toolkit which allows you to create and run text games.
InterAx – Create first-person adventure games with no scripting.
SLUDGE – A simple scripting language for creating adventure games. It isn’t the most intuitive option, but it is definitely functional.

RPGs

RPG Maker 2003 - A classic, easy-to-use RPG designer.
RPG Toolkit Development System – A free, open source system for creating RPGs.
Sphere – Sphere requires quite a bit of scripting, but with that comes a lot of flexibility. The engine is ideal for Final Fantasy style RPGs.
Official Hamster Republic RPG Construction Engine – This one has been around for ages, and for good reason - it’s a great option and has maintained an active community of developers for years.

General 2D

2D Shooter Game Creator – I didn’t try this one, because they seem to want me to pay for it. Plus they really like using red italicized text. But here it is for the sake of completeness.
Clean Game Library – Clean is a programming language/compiler, not a simple “point-and-click” game creation system. It will take some time to learn and implement the language, but the example games look promising.
Game Maker 7  – I covered this one on the last page – it is a very clean, full featured 2D game development platform.
Multimedia Fusion – A very feature rich, but pricey, toolkit for developing interactive applications. Because my intent is to get you started in basic game design before you move on to more complex stuff, and not to replace simple code with expensive software, I can’t highly recommend this.
Scrolling Game Development Kit – A complex but learnable toolset for the creation of side-scrolling games.

General 3D

3DCakeWalk – A 3D game engine with lots of prewritten code, as well as the option to write your own scripts in Python. Unfortunately, the site reveals little about the toolkit, no demo appears to be available, and it hasn’t been updated since 2007. If any of that changes, it may be worth checking out, but otherwise it might be abandoned. There appears to be an old demo version here.
The 3D Game Maker – “Make Horror games with 3rd person controls and scare yourself silly!” This is so point-and-click simple that it’s more of a game itself than a game creation toolkit, but it might be entertaining if you’re willing to buy it.
3D Rad – The supposed “high-quality rendering” is a bit dated, but 3D Rad is nevertheless a functional, if somewhat simplistic, 3D game engine and creation toolkit. According to the site’s front page, the download is a 30-day trial, but the download page proclaims: “The 3D Rad free download can be used freely for commercial and non commercial purposes.”
Blender – Free, open source, and amazing. Blender is a professional quality 3D modeling, animation, and game building toolkit.
Antiryad Gx – A solid, free 3D game engine. Note that, like many other 3D engines, this won’t do much for a complete beginner.
DarkBASIC – A reasonably priced engine which utilizes a modified, easy-to-learn version of the BASIC programming language. At one point (before being sucked up into “The Game Creators”) a free, trial version was available, but it is no longer being distributed. Cnet, however, has an older trial version available for download.
FPS Creator – “…you can't find a better and more easier product." – a testimonial on the site. That should give you an idea of the audience that FPS Creator caters to – but don’t knock it right away – it’s pretty fun to play with. I just wouldn’t suggest that you can use it to realize your creative vision.
Game Studio – According to the site, “Game authoring never was easier.” That may not be entirely true, but Game Studio is worth checking out – even Atari was in on it. The programming language – Lite-C – was designed to be quick and easy, and the system can produce some very nice-looking games.
Silent Walk FPS Creator – A clean, simple, and overall very nice FPS development kit. I used it until I started getting a “memory access violation” when I ran my game… but it was probably something I was doing wrong. The download link is at the bottom of the page. Unless you register your copy (for
 $24.99), your game will contain big watermarks.
Reality Factory – Several applications aimed at creatives who don’t want to touch a line of code. The graphics aren’t top of the line, but it’s worth taking a peek at.

Online

Byond – A simple scripting language which allows you to create multiplayer online games, which are played through the Byond software.
Realm Crafter – Realm Crafter is actually a large set of tools meant to ease the difficulty of building an MMO. There’s too much stuff here for me to try all of it, but a free demo is available if you want to play with it. The full software is pricey.