I don't think being on the very ends of a snake draft is very good at all. Nor is being in the middle. If you are targeting a specific player in the first round, then you obviously want to draft with the last pick you think he'll still be available, but I wouldn't base my draft strategy on the first couple rounds, which are all that have been mentioned here.
The best draft positions are two or three picks away from either end of a snake draft. The longer you have been in a league and the more you know the other owners the better.
The first thing to do is to identify tiers of players at each position. Keep a list of each position organized by tier. The other important thing to do is to keep track of how the other owners in your league are filling out their rosters, and which positions and categories they still need to fill.
If you are near, but not at one of the ends of a snake draft, you'll probably have one to three teams having double picks inbetween your closest two picks which occur every other round. That means you'll have two to six players that will be taken off the board inbetween your closer set of picks in any two rounds.
With just one to three teams' needs to take into consideration, you can make educated guesses as to which players will be taken in those two to six picks.
The draft is still about market value for a player--getting the best players as possible as late as you can get them. If you know you can get someone in round seven, under no circumstances should you take them in round six, even if they are worth a sixth round pick. Grab someone else in the sixth who is also worthy of that pick and get the second sixth-round-worthy player with your next pick in the seventh.
If you have kept track of what everyone has taken, you can really make some good predictions and help yourself out, especially in the middle rounds, after the no-brainer studs have been taken in the early rounds, but before people have filled their line-ups and have begun to take reserves.
Now is when you need to pay attention to the tiers of players you have identified.
Here is an example: I'm picking 9th in a snake draft of 12 people, I still need a starting shortstop and my first good closer. We're in the 7th round. I notice that there are only two players left in the second tier of shortstops, and only two second tier closers remaining as well. I know that three teams are going to be making a total of 6 picks inbetween my 7th and 8th round picks. I check the list I've been keeping of which players each team has taken.
I notice that teams 11 and 12 both already grabbed shortstops in the first two rounds, let's say Nomar and Renteria, even though the specific players are unimportant. However, none of us, teams 9, 10, 11, or 12, have taken a closer yet. So, I decide to take etheir Octavio Dotel or Jason Isringhausen over Kaz Matsui or Angel Berroa.
The reason being is that only team 10 is likely to use one of their two picks on a shortstop, as teams 11 and 12, with Nomar and Renteria respectively, would be unlikely to grab Kaz Matsui or Berroa when they still have holes to fill in their starting line-up. The odds of either Matsui or Berroa falling to you in the next round, round 8, are pretty good, as only team 9 will be likely to take a shortstop.
However, you and the other three teams left to pick in round seven all still need closers. The odds of either Dotel or Isringhausen being on the board by the time you pick in round 8 are scare.
Thus, you grab Octavio Dotel, watch Isringhasuen, Kaz Matsui, a third tier closer, and three other position players get taken, and grab Berroa with your 8th round pick.
You wound up getting two of the few second tier players at their positions because you guessed correctly that more than just two closers would be taken and fewer than two shortstops would be taken between your next two picks.
Being at the end is the worst. Sure, you get to double up, and people will tell you there is good value at the end of the first and begining of the second, but you have absolutely no clue who is going to be on the board the next time your set of picks comes around. Being smack dab in the middle of each round makes it tough as well. It is easier to predict what two teams will do than four or five.
That is just what I think. My keeper league goes off of the previous seasons standings. I came in third to I'm happy to wind up two spots from the end of round one.
That, and I haven't seen any correlation with position in the first two rounds of a snake draft and league championships. If there was, we probably would have heard of it by now. There has been no discernable pattern in my keeper league, even before it was a keeper league.
I'd rather be able to forecast a couple of opponents picks every other round.