I've been skipping through some episodes of DBZ, andtwo things are constant throughout. Vegeta is cocky and Vegeta loses. It's not even such a big deal that he loses, but he acts like he never loses. He doesn't even fight against the odds because it is what an honorable warrior does. He just has delusions that he will win every fight.
This list is comprised from my memory and what I've seen skipping around so far (insignifcant or assissted wins are ignored):
Vegeta makes his first appearance on Earth and fights Earth's defenders, who are all outclassed by him, besides Goku.
Loses to Goku/Gohan, 0-1
Vegeta visits Namek to continue his quest for the dragon balls.
Loses to Zarbon, 0-2
Vegeta is assisted by some convenient ret-conning. Suddenly, super sayans are made to be even stronger after recovering from a fatal injury. Goku lost many battles as a child, but was never made stronger from them. I guess the writers felt that Vegeta needed a handicap.
Defeats Zarbon, 1-2
Vegeta shits his pants for once and recognizes when he is outclassed in a rare moment when the Ginyu Force arrives.
Loses to Recoome, 1-3
Vegeta gets cocky on the power of writer's assistance and thinks his recovery will let him beat Frieza just like how it helped him beat Zarbon. Frieza easily disbatches Vegeta. Vegeta manages to spit out his sob story to Goku. This moment is meant to humanize Vegeta and make the viewer realize that Vegeta was actually a victim of Frieza and had no chance to be any other way. Viewers knew this moment well. It was the same kind of moment Piccolo had against Nappa. However, these were just meaningless dying bitch tears. Vegeta will not learn from this after being revived later.
Killed by Frieza, 1-4
Vegeta trains non stop to become a super saiyan, crying that Goku achieved it before him. Once he reaches it, his ego also becomes a super saiyan. This is sadly fed with his defeat of Android 19, the weakest of all androids.
Defeats Android 19, 2-4
Vegeta is being repeatedly told by Trunks that Android 17 and 18 are far too powerful for him. Trunks is telling him that in his time, Vegeta and all the other fighters have been killed by them, and these versions of the androids are even stronger. He literally has somebody from the future telling him what will happen. But his ego will not be stopped and he is quickly left with a broken body by Android 18.
Loses to Android 18, 2-5
Vegeta trains in the Hyperbolic Time Chamber for a year and his ego is recharged. He has no idea how strong Cell is now, but still believes he is destined to win.
Loses to Cell, 2-6
Vegeta watches his son be murdered by Perfect Cell. Goku, his greatest rival, sacrificed himself to stop Cell, while Vegeta refused to even acknowledge Trunks as his son, who simply wanted to save his father as well as to get to finally know him. Both Goku and Gohan have suffered great losses in battle. Both of them reached new peaks from them and defeated foes that easily outclassed them. Vegeta just puts on a meaningless fireworks show before being one-punched by Perfect Cell. This moment was meant to try and re-humanize Vegeta. It proves to fail again later.
Loses to Perfect Cell, 2-7
Vegeta can't stop being mopey over how his birthplace doesn't give him everything like he was told. When he sees Goku again after several years, he sees that he is still no match for Goku. The only logical conclusion is to do something equivalent to selling his soul to the devil for strength. Even in this form, he still cannot beat an already-dead Goku who is simply defending himself against Vegeta.
Fails to defeat Goku, 2-8
Vegeta underestimates Maijin Buu and is beaten.
Defeated by Maijin Buu, 2-9
Vegeta fights Kid Buu in an act of desperation, but loses as expected.
Defeated by Kid Buu, 2-10