At some point in during my MSc degree, our postdoc inducted me into the Molecular Sieves Cult (lets also call this MSC for short). I needed dry solvent and the postdoc handed me a printed copy of Drying of Organic Solvents: Quantitative Evaluation of the Efficiency of Several Desiccants. This paper has been the second most useful one in my career (after NMR Chemical Shifts of Common Laboratory Solvents as Trace Impurities).
Here is where I should probably put my conflict of interest:
My group job is to refill and maintain our solvent purification system (SPS).
Fewer people use it = Less work for me
I joined the MSC long before this group job though. As the Paper says, mol sieves and time are better or equal to distillation or the neutral alumina in a SPS. You also avoid the danger of distillation and the large startup cost for an SPS; all you need is some cheap mol sieves and a bottle! I have big bottles of dry DCM, MeOH, and toluene that believers in the lab use (but never refill...) and small bottles of MeCN, EtOH, iPrOH, and ethylene glycol.
I believe that 3A mol sieves are essential to every lab and I hope to convert others to the MSC, but now I'm going to talk about the dark side of our cult.
The most memorable blog post I've ever read is by the Curly Arrow titled Anhydrous Solvents Part 3: Acetone and Molecular Sieves - Bad idea! It's a great post and essential reading for MSC members. In short: mol sieves are slightly basic and over time it'll Aldol the heck out of acetone to make heavy, greasy crap.
THF & Other Ethers
The point of mol sieves is that you can set it and forget it. Forgetting ethers in a bottle on the shelf for long periods of time can lead to peroxide formation, so I avoid using it or only dry the amount that I'll need for that week.
DMF & Triethylamine
These tend to turn brown over time. If I were to buy an SPS the only solvents I would have are DMF (since it loooves water) and THF (for BuLi reactions). If you need very dry triethylamine just do what I do: Go to Zakarian's lab and use his solvent still ;)
A Note about CDCl3:
Like most people in the MSC, as soon as I crack open a cold CDCl3 with the boys I dump in pile of mol sieves. Say goodbye to water in your 1H NMR (unless your compound is still wet) and since it's basic it should in theory mop up any DCl.
One very hot summer, I was trying to assign some very small peaks in my 13C NMR. I found a tiny peak hidden in the residual solvent peak and called it a day. In the coming weeks, the peak was growing. I ran a blank 13C NMR and then went back and reassigned my spectrum.
The problem is that our lab gets hot during heat waves. Like really, really hot (35 C)! I never found these peaks during "winter" or non-heat-wave-summer. I suspect that when heated, the water trapped in the sieves was doing a base-catalyzed hydrogen exchange. This is just a theory, and I haven't put in the effort to replicate it. They also upgraded our lab so it doesn't get as hot now - just in time for me to graduate :/
Don't let these exceptions scare you from mol sieves, they're amazing as long as you are using the right solvents. If you have strong feelings about the MSC or any solvent-specific knowledge please let me know in the comments below!