Street Fighter II Beginner Tutorial - Most of the basics of Street Fighter haven't changed over the years, so the concepts explained here are still very important to understand. Street Fighter IV does have advanced techniques beyond the scope of Street Fighter II, and you'll find videos explaining those techniques a little latter. I've also excluded the second part of the beginner tutorial, as almost everything explained does not apply to Street Fighter IV.
Street Fighter II Intermediate Tutorial - This video covers combos, cross-ups, reversals, and more.
Street Fighter II Advanced Tutorial - overheads, piano inputs, the fact that letting go of a button can also activate specials and supers, and more.
Street Fighter IV Combo Tutorial - A detailed explanation of all the ways you can put a series of moves together to form a combo.
Street Fighter IV Focus Attack Video - How to use the focus attack, dash out of a focus attack, focus attack into an ultra, focus attack cancel a move to juggle your opponent into the air, and more. Despite what is said at the end, no other videos in this series were made.
The last two videos here mostly cover techniques that have already been covered, but there are a few important additions that have not been talked about, such as some advanced throwing techniques.
Finally, please consider this a supplement to the existing Giant Bomb Street Fighter IV Beginner's Tutorial, which can be found here:
The videos above are really more of a quick introduction to SSFIV. The guide in the link above goes into even more detail. While the videos don't go into quite as much detail as the text, they do show you an actual controller in the hands of a player, which should be helpful in implementing the techniques you've seen in the videos above.
I hope this was helpful to any new players. If anyone knows of some other good tutorial videos that cover topics not explained above, or if you feel they just explain things in a better way, feel free to post them below. Any good individual character videos might also be a good idea for this thread. How to play a character well, not just insane combos without explanation, of course.
Please check out some of my 3-minute fundamentals covering aspects of Street Fighter IV (these are still applicable to Super Street Fighter IV). I will be making more in the near future once I get some better recording gear for consoles. Stay tuned for that.