I'm basically in Bleppe's situation ("computer guy" who never really got around to learning how to program, then the Rift happened) but perhaps a few months ahead of him on my journey. The important question is this: If "making games" is your goal, are you entirely certain you want to approach that from the programming end? I'm not an industry insider, but I think most people who are will tell you that the guys doing actual programming usually comprise a tiny segment of the workforce involved in producing any kind of modern game. Art assets take the most man-hours to generate in most circumstances, and the people doing that don't need to know how to program so much as a microwave. 3D modelers, texture artists, animators, level designers, sound engineers, and testers "are" the contemporary video game production staff; the programmers are commonly regarded as just a couple of nerds in the back room who glue all of that stuff together. Solo developers are finding some success putting out Rift demos right now, but that's mostly because there isn't much professionally produced VR content yet, and we're all starving for more. In a few months, I expect we'll be mostly back to the status quo: If you aren't part of a talented and hardworking team, not many people are going to pay much attention to your tech demos, assuming you're able to finish anything in the first place. It's a tough nut to crack, because joining a small studio or building a competent team around yourself requires that you have and can demonstrate valuable skills, and building a portfolio isn't easy when you have to be a designer, modeler, artist,
and programmer.
If your primary aim here is personal enrichment, great - programming is a fantastically valuable skill to have (just don't be too hopeful you'll have much to share for the first few
years of effort). If you either want to publish games ASAP or find a career in game development, however, you're much better off focusing on an aspect of game design that isn't generally regarded as something that takes ~10 years to learn. Attaining some level of competency with modeling and/or animating in Autodesk's
industry standard tools (or the freeware
Blender) may only take a few months, and may not even require traditional artistic talent. If you have some of that, the world needs more
texture artists; if you find even modeling beyond your abilities, track down some map creation tutorials for UDK and see how you enjoy the level designer role. The easiest (and least enjoyable) way to enter the video game industry is to become a playtester, but just about any role is easier to break into with zero prior experience when compared to the programmer role.
If, after all that discouragement, you're still set on learning to program, welcome to the club.
Personally, I highly recommend starting out with
Python. geekmaster's probably right (as usual) about starting from the bottom - if you could recreate the computer you're using with a pile of transistors and a soldering iron, the code you write will probably be bulletproof. Taking that path means you won't get anywhere near anything that resembles a game for a few years, though, and I personally didn't have the resolve to slog through all that book lurnin'. You'll definitely want to wind up knowing C++ eventually, but it can be a nightmarish place to start if you don't have a grasp on some fundamental programming concepts. C# may not be a bad choice for a first language, but I suspect the reason it's cited as a "popular" language is that it makes producing internal corporate crapware "faster"; its only role in the game industry seems to be with Unity, and while Unity definitely has its merits, it also has some major drawbacks (not the least of which is the $1500 you'll need to pay to even get started developing for the Rift). Javascript is also a decent place to wind up, but not the best place to start - it (justifiably?) gets a lot of flak for having mindbending syntax, and despite making you do a lot of the low-level memory management stuff that makes starting out difficult, it's impossible to optimize to the levels required by cutting-edge engines.
Personally, I love Python because it sweeps many of the things neophytes find challenging under the proverbial carpet; whitespace delimitation is infinitely less frustrating than playing "find the missing curly brace and/or semicolon" for hours on end every time you build something, it's an
interpreted language so you don't have to wrestle with a compiler
and your bug-infested code, and the memory management stuff it hides isn't anything you're likely to master when you're first learning what a "for" loop is anyway. The best part is, once you've written a bunch of toy Python programs and you're ready to graduate to C++ or whatever else, the vast majority of what you'll encounter will seem like review, and you'll often find yourself still doing a lot of Python scripting in instances where you don't need to finesse every electron for maximum performance. I can't say how well Python knowledge translates into the Unrealscript or Torquescript proficiency you'll need to actually produce working game code, but I think someone comfortable with Python will be in a much better position to understand them than someone trying to start out at their eventual destination.
TL;DR: "Making games" is more than just programming these days, so that may be something to explore first. If you're determined to learn to program, that's great, and so is Python. 
