I got this from looking around at the forums at tv.com. You can watch most episodes in three parts. Type in the following URL into your address bar without pressing enter:
http://media2.yahoo.com/player/ligans/?key=
After the equal sign, put in the code corresponding to which part of an episode you want to watch.
The Great Gladiator Gig: 49192, 49193, 49194
Mario and the Beanstalk: 47614, 47615, 47616
Love ‘Em and Leave ‘Em: 47641, 47642, 47643
The Great BMX Race: 47576, 47577, 47578
Two Plumbers and a Baby: 47724, 47725, 47726
Pirates of Koopa: 47738, 47739, 47740
Robo Koopa: 47741, 47675, 47742
Count Koopula: 47727, 47728, 47729
Jungle Fever: 47735, 47736, 47737
Mario of the Deep: 47730, 47731, 47732
Mario Meets Koop-zilla: 47746, 47747, 47748
Mario and Joliet: 47733, 47734, 47633
Too Hot to Handle: 47627, 47628, 47629
Brooklyn Bound: 47617, 47618, 47619
The Adventures of Sherlock Mario: 47679, 47680, 47681
Hooded Robin and His Mario Men: 47630, 47631, 47632
Toad Warriors: 47686, 47688, 47690
The Pied Koopa: 47656, 47657, 47658
Bad Rap: 47608, 47609, 47610
On Her Majesty’s Sewer Service: 47645, 47647, 47648
Mario and the Red Baron Koopa: 47611, 47612, 47613
Mighty McMario and the Pot of Gold: 47669, 47670, 47671
Do You Princess Toadstool Take This Koopa…?: 47692, 47693, 47694
The Mark of Zero: 47704, 47705, 47706
20,000 Koopas Under the Sea: 47676, 47677, 47678
The Koopas Are Coming! The Koopas Are Coming!: 47620, 47621, 47622
Koopenstein: 47682, 47683, 47684
Quest for Pizza: 47663, 47665, 47667
The Unzappables: 47700, 47701, 47702
The Trojan Koopa: 47697, 47698, 47699
Karate Koopa: 47637, 47638, 47639
Elvin Lives: 47624, 47625, 47626
The Ten Koopmandments: 47652, 47653, 47654
The Provolone Ranger: 44709, 44710, 44711
The Great Gold Coin Rush: 44701, 44702, 44703
Mario of the Apes: 44685, 44686, 44687
Koopa Klaus: 44689, 44690, 44691
Crocodile Mario: 44693, 44694, 44695
Plumbers Academy: 44681, 44682, 44683
Princess, I Shrunk the Mario Brothers: 44713, 44714, 44715
Flatbush Koopa: 44697, 44698, 44699
Raiders of the Lost Mushroom: 44705, 44706, 44707
Star Koopa: 45428, 45429, 45430
Escape From Koopatraz: 45630, 45631, 45632
Little Red Riding Princess: 46520, 46521, 46522
I unfortunately do not have codes for The Bird! The Bird!, King Mario of Cramalot, Butch Mario & the Luigi Kid, Mario's Magic Carpet, Rolling Down the River, Stars in Their Eyes or The Fire of Hercufleas.