Chain rolls
When my group started looking into playing some Exalted vs the World of Darkness, I started getting flashbacks to my old days of playing Vampire the Masquerade and the old mechanics that are still in that system. Of them, the most pertinent to our discussion today are the attack rolls.
To attack someone in Vampire the Masquerade, you roll your Dexterity and say, Melee. If you succeed, you take however many successes over 1 you got, add your Strength and the damage of the weapon you are using, and roll that again. That is the amount of damage you do. Now the enemy makes their soak roll and subtracts the successes from your attack roll. So you roll three times in order to get the result you want (you can also start adding the cost-benefit analysis of various manoeuvres like "if I strafe with my assault weapon and get +10 to hit but +2 difficulty, is that a net gain for me?" but let's keep it simple...).
Now, let's compare that to Vampire the Requiem. You roll Strength + Melee - your opponent's Defence. The amount of successes you roll is how much damage you do. Done. In one roll you accomplish everything you used to in three rolls.
This type of rule design can really speed up how you resolve each action in combat without lowering the depth of character builds. You can still make glass cannons, soak tank and what have you.
Try, try again
A thief walks up to a lock. They roll to pick the lock, and they fail. They roll again, and they fail. Someone else from the party decides to give that same lock a try, they roll, and they fail. Then the thief rolls again, succeeds and the party moves on.
A lot of you could probably think back to something like this happening in your game, probably even the exact same scenario. It's an example of a roll that's not impactful if you fail it. Sure, if you only had one chance to pick that lock, that would be something, but if you're picking a lock that's the only way through to continue your adventure, failure is not really an option.
There are two ways of addressing this issue - either ignore the roll entirely if the characters are skilled and equipped enough for it to not be a challenge, or think of some meaningful consequences for failed rolls.
The first approach can be found for example in the Vampire the Masquerade games - if your dice pool for a roll exceeds the difficulty of the roll, you automatically succeed at the roll (under certain conditions). Even if your system doesn't support it, you can usually tell when some roll is beneath your player's character - just roll with the fiction and move on.
The second approach is very prominent in the Powered by the Apocalypse systems like Fellowship. Each time you fail a roll, either there are set consequences to be had, or the GM can use Cuts against you. Maybe they'll "Show signs of an approaching threat" - you made noise and attracted the guards to your location, or "Use up or take away their resources" - your lock pics gear breaks and now you have to batter the door down, etc.
At any rate, you want the roll to be important, whether it succeeds or fails. If it's not important, it's not necessary.
Conclusions
If you can help it, try making every roll in your game be meaningful and impactful. Sure, sometimes it's fun to ace a roll you're really good at, but you can just as easily narrate how awesome you are when you auto succeed. Try giving your rolls weight for failure beyond "nothing changes" - that outcome is the most boring of them all.