Not a new one, but...
New York and Boston players are always overvalued.
Actually new one:
Never, EVER, think in a draft 'i sure wish i could grab that player who's fallen a stupid distance, but I really need a third baseman/closer/starter here before they're all gone.' There will usually be at least one undrafted/late round guy who will put up league-average numbers, but the guy who gets the falling studs wins the league.
Write 'I will not draft Mark Prior' out 100 times before beginning any draft.
I actually strongly disagree with the 'do not draft closers before round ten' thing. Draft one closer you know to be good, between the seventh and tenth rounds, then don't bother with the Mike Adams and Dan Micelis of this world. I wasted a couple of good picks on guys who lost their jobs within weeks, when I could have much improved my third outfield slot, for example. But Trevor Hoffman has been a rock for several teams.
In holds leagues, don't chase that cat AT ALL. Relievers are notoriously unreliable. Throw some very late-round mud at the wall.
Never play a H2H league that doesn't have roster move limits of 75 at the absolute most.
Multiple position eligibility isn't that important for guys who will play every day, but huge for bench players.
Playing an NL only league, if an AL fan, or vice versa, is great for deepening your knowledge.
Target players who suffered impact injuries. These can keep a guy out and off the radar for a long time, but don't generally affect him long-term.