Assuming I have all the math right, this should be a fairly complete list of the possible cooldowns on most of the summoner spells.

It is a lot of information that I wouldn't expect most people to encode. This is more of a baseline that I can work with to distill down and gave me a chance to play with tables.

It is interesting information if you think of say Sona running Flash and 3 points in Summoner's Insight and wearing Enchantment: Distortion on her boots, she can Flash Crescendo your team every 3 minutes and 30 seconds, which is a big difference compared to every 5 minutes.
Sumnmoner Spell Base Cooldown (s/min) Base + Summoner’s Insight (s/min) Base + Distortion (s/min) Base + Distortion + Summoner’s Insight (s/min)
Barrier 210 / 3:30 189 / 3:09
Clairvoyance 60 / 1:00 54 / 0:54
Clarity 180 / 3:00 162 / 2:42
Cleanse 210 / 3:30 189/ 3:09
Exhaust 210 / 3:30 189/ 3:09
Flash 300 / 5:00 270/ 4:30 240 / 4:00 210 / 3:30
Ghost 210 / 3:30 189 / 3:09 168 / 2:48 147 / 2:27
Heal 240 / 4:00 216 / 3:36
Ignite 210 / 3:30 189 / 3:09
Smite 60 / 1:00 54 / 0:54
Teleport 300 / 5:00 270 / 4:30 240 / 4:00 210 / 3:30
Teleport to Tower 240 / 4:00 216 / 3:36 192 / 3:12 168 / 2:48
Teleport Interrupted 200 / 3:20 180 / 3:00 160 / 2:40 140 / 2:20

I would list the following summoner spells the most important to time.

Flash 5:00
Barrier 3:30
Teleport 5:00
Heal 4:00
Exhaust 3:30
Ignite 3:30

If I were try to categorize that to make it a little bit easier I think it would be like this:

Mobility Summoner = 5:00
Combat Oriented Summoner = 3:30
Heal: 4:00

They represent windows of potential opportunity.

E.g. You and your ADC manage to get the opposing laners to blow their Heal and their Exhaust so you have about four minutes to take advantage of that situation.

Same situation as written above and their top laner just Teleported back to lane.

Even better! You can go ham and if you get low you don't have to worry about their top laner showing up for the turn around.