The accepted rule is boiling with the lid off, or dimethyl sulfide (DMS) can't escape, and can leave a cooked corn or vegetal off flavor.
DMS is created in hot wort, and comes from the precursor compound SMM that's naturally present in malt. Certain malts have more than others, usually corrolated to the color and processing of the malt. Darker base malts and specialty grains have very little, pale base malts have more. Generally Pilsner malt has the most. When boiling, the DMS is driven off in the steam. If you don't boil long enough, or if you allow the steam to condense and drop back in (boiling with the lid on) you can end up with excessive DMS in the finished beer and off-flavors as a result.
When you're getting your wort from grains, you should be boiling at least 60 minutes with the lid off, or 90 minutes if you're using Pilsner malt. When brewing with extract, it's not as important, as much of the SMM is converted to DMS and then driven off as part of the manufacture of the extract. You can do shorter boils, and if you need to keep the lid partially on (or while I still wouldn't recommend it, on entirely), it'll have less of a detriment.