Most routine checks for me include:
Temp, pH, Calcium and Alkalinity and Salinity (once a week).
Next off includes:
Phosphates & Nitrates (now and then...)
and then:
Strontium & Iodine (infrequently, I'd say)
...the frequency of the tests I do are based both on how often I modify certain constituents (based on test results of course - kind of a feedback loop, eh?) and how apt they are to change on thier own due to environmental circumstances... (ie, kalkwasser dosage, rate of calcium uptake by corals, rate of water evaporation, hot summer days, water changes, heavier than normal feeding, etc...)
I'd highly recommend getting a good book on the subject, as there really is a hell of a lot to cover, and a few exchanges like this might not cover it for you before you get too eager and make mistakes. Also, search the database at reefs.org, there's loads of good info. It really depends on what kind of tank you intend to maintain - some factors are more important than others depending on the setup.
I'm running a 90 gallon reef with live rock piled to the top & moderately intense lighting (need more!). Mostly leathers, shrooms, polyps and LPS corals in there... A very few happy little fish, a reef lobster, cleaner shrimp, and handfuls of various snails as well... Loads of purple, blue, green and red coraline algae.
By contrast, a fish only tank requires less testing. Other guys who've got loads of SPS corals and kick ass lighting, etc...,might test more... Again, it all depends...
