To give you a little history on me, I've played SR off and on since 2E. I liked SR before, but have only fallen in love with it since the advent of 4E. I feel the newest edition is an improvement over the old in almost all ways: the setting has been evolved and revitalized while keeping the soul of the original, the setting supports a wider variety of concepts and doesn't force archetype specialization, and the system is cleaner and easier to understand. I bought the 4E core, Augmentation and Street Magic more than two years ago, but ended up gifting them to a friend (who now uses them as paperweights as far as I can tell). I've kicked myself ever since, and so recently I've reinvested in the 20th Anniversary Edition, Runner's Companion and Street Magic. I plan to round out my collection with Arsenal, Augmentation and Unwired here soon, and perhaps other books in the future. And I won't be giving those away, I can assure you.
Anyway, point at hand: while I like the newer mechanics (it's probably my favorite system period) and think it's an improvement over previous editions, there are two things I miss: exploding dice and exploding initiative passes. Let me explain what I'm talking about and my thoughts on the issue.
Exploding Dice: I'm playing in a 3E game now, and as ever it's a lot of fun to roll the dice, hit 6s, and keep rolling, accumulating ever-higher numbers. Now that's not really necessary, as the system doesn't have sliding target numbers anymore; a 5 or 6 is a hit. You can reroll 6s when you spend Edge, and those hits add to what you have. Simpler, quicker, cleaner. Though I can't really justify this from a pure mechanical standpoint, the accumulating successes were fun. I've considering ways to possibly bring that back to a limited degree, without breaking the system or messing with the hits setup. Note my desire to see the exploding dice is a preference, perhaps a holdover of old habits, not an attempt to address something wrong with the system.
Option #1: All die rolls explode -- 6s are rerolled. Each 6 rolled is another hit (not 5s, only 6s) and allows another reroll; if any of these dice are 6s, you can roll again, and so on. You can never attain more "exploding hits" than your relevant attribute or skill rating (whichever is higher), however.
Then how is Edge useful? When you spend Edge, your rerolls let you treat both 5s and 6s as hits (as per normal die rolls), and your potential extra hits aren't capped.
Option #2: Die rolls explode, and you add the result of the rerolls to previous 6s -- like in previous editions. If you get a 15 or higher while rerolling, you get an extra hit; if you get a 25 or higher, you get yet another hit, and so on for each iteration of +10 (35, 45, gods forbid 55). So if you manage to reroll your way to a 26, you get two extra hits (one for beating 15 and another for beating 25). This is more manageable than the previous option, as it'll result in fewer extra hits overall, and reduces he need for arbitrary hit caps.
Option #3: It ain't broke, stupid. Don't fix it.

Option #4: You reroll 6s and add reroll results to previous 6s. If you roll "really high" (in the opinion of the GM and other players), you take a shot of liquor. If you get a super-duper high result (again, by group estimation), you take two shots. If at any point you roll three 6s, you must put on the devil cape and horns provided by the GM, brandish a plastic pitchfork, do the naughty Devil Dance and take a shot. If you're conscious at the end of the game, you win. Take a shot.
Any of these workable?
Exploding Initiative Passes: This, I think, I miss the most. In previous editions (as most of you probably already know), you rolled 1d6 and added your Reaction; some augmentations, Adept powers and spells allowed you more dice on this roll. Every iteration of 10 you scored, you got one extra initiative pass. So if you got 23 on one initiative roll, you got two extra initiative passes. If you only got 18 on your next roll, you got one extra action. I really like this, because there was a certain randomness to combat. Even if your Reaction wasn't that great and you only had a single die to add, if you were lucky and rolled high you could act twice that round; and some excessively wired sam used to going three times a round might only get two actions, or even one, depending on how the dice shake out. The number of actions one can take wasn't set.
Now, your number of actions are set. A character without a power or upgrade of some sort that allows extra initiative passes never gets them (save for Edge expenditures). And someone with certain qualities will always get extra passes. If you astrally project, you get three passes. While simple and easy to manage, this lacks appeal to me. . I'm willing to deal with extra complexity if it means recreating the semi-chaotic feel of the old initiative pass setup.
The question, would patching something like this into the 4E rules be possible without gutting the system? It seems it shouldn't be too much trouble, but I'm appealing to others that may know the system better than I or that have done the same thing.
The last word of my display name isn't capitalized, hoping to get ten posts quickly so I can fix that!