Global skills (not to be confused with skills) can be bought with green shards, but only when you are not in a challenge or endless mode. Each new global skill purchased additively increases the price of all global skills by 10%, and each upgrade increases the prices by a further additive 1%. Here is a list of them with all manner of useful information:

Global Skill Effect Base Cost of Level X Max Level
Cheaper Buildings Reduce the progression of buildings cost by 1 percent 100^X 5
Faster Science Reduce the time needed to complete researches by 10 percent 55^X 5
Harder Clicks Increase critical hit power by 10 percent X^7 10
Frequent Bonus Decrease waiting time for next bonus by 20-40 seconds X^7 10
Critical Chance Increase critical chance by 2 percent X^9 5
Refresh Decrease waiting time for the next click by 10 percent 77^X 5
Producer Increase GPS by 10 percent X^4
Clicker Increase GPC by 10 percent X^4
Starter Increase GPS by 1 X^3
Booster Increase GPC by 5 X^3
Faster Start Increase your initial gold in bank by 100 3(X^3)
Rusher Increase Gold Rush bonus multiplier by 1 X^10 5
Toucher Increase Perfect Touch bonus multiplier by 1 X^10 5
Rager Increase power of Critical Rage skill by 30 percent X^10 5
Longer Rush Increase duration of Gold Rush bonus by 10 seconds 3(X^6) 15
Longer Touch Increase duration of Perfect Touch bonus by 10 seconds 3(X^6) 15
Longer Rage Increase duration of Critical Rage skill by 6 seconds 3(X^6) 15
Slower Make bonuses fall x2 slower and adds warning before bonus appears 2(X^7) 5
Collector Increase number of shards gained during explosion by 10% 2^X
Detonator Significantly increases shards from explosion in case of early detonation 3(X^10) 5
Damager Increase DPS by 10 percent X^5
Piercer Increase DPC by 10 percent X^5
Destroyer Increase critical damage power by 10 percent ? 10
Damaging Rush Gold Rush increases DPS by 100% ? 7
Damaging Touch Perfect Touch increases DPC by 100% ? 7
Damaging Rage Critical Rage increases critical damage power by 30% ? 7
Timer increases a chest challenge time limit by 2 minutes ? 10
Richer x10 gold from pure benefit skills ? 7