Actually I did look at it, since 2000, you might not believe it but Tigers have best all-time finals record of 6 wins from 9 games (66.67%). It helps when you win the GF on 1 of your 3 finals campaigns.
Roosters are 17/26 in this time (65.38%) and Melbourne are 17/28 (60.71).
Parra come 4th with 10/17 (58.82%), and every other team are 50% or less.
Broncos surprise me, but they did have a few bad campaigns I suppose: 13/28 (46.43%). Even Dogs are surprising 11/23 (47.83%) though they've made grand 3 finals in this time.
Every team has played at least 4 finals games since 2000, with Raiders and Titans are the worst win record, 3/12 and 1/4 (25%) respectively.
Also interestingly, of the 13 teams to make a Grand Final since 2000, 6 of them have perfect GF records (Tigers, Souths, Knights, Broncos, Panthers, Dragons) and only 1 of those has played more than 2 GFs (Broncos with 2). Cowboys are the only single-appearance side not to win, with Warriors and Eels the only other sides to appear but not lift the premiership (twice each).
The teams that have made several grand finals have more modest records - since 2000 only Melbourne has made more than 3 GFs (5) and won more than 50%.
The other interesting trend since 2000 is that the two teams that have made the GF the most times - Roosters (6) and Storm (5), both lost their first GF appearance (ignoring that Melbourne actually won it in 1999, we have to draw line somewhere) and actually make up 40% of all GF losers in this period.
Thus recent history predicts, if Sharks make the GF this year, they are a really good chance of winning it, and I would not be surprised to see them face off against Roosters or Melbourne.