There aren't any Pokeballs as good as a Master Ball, but there are Pokeballs that do better under certain conditions.
Diveball ~ Higher chance of catching Pokemon if it is from the water. *From Fishing Rods and surf*
Dusk Ball ~ Has a better chance of catching Pokemon while at night.
Great Ball ~ Has a better chance of catching a Pokemon than a Pokeball. It can be used at any time and the chance of getting Pokemon won't change.
Heal Ball ~ (Capture rate may be the same as a Pokeball) It heals the Pokemon when it is captured.
Luxury Ball ~ Capture Rate is the same as a Pokeball. It raises the Happiness Stat of a Pokemon upon being captured.
Master Ball ~ Captures Wild Pokemon automatically.
Nest Ball ~ Likely to capture Pokemon with lower levels easily.
Net Ball ~ Has a higher chance of capturing Bug and Water Type Pokemon.
Premier Ball ~ Has a normal chance of capturing a Pokeball
Quick Ball ~ Has a higher chance of capturing Pokemon, the earlier you use this ball.
Repeat Ball ~ Has a higher chance of capturing the Pokemon if you've caught one of its same kind already.
Timer Ball ~ If you use this in the later turns of your battle, the likelier you'll catch the Pokemon with this.
Ultra Ball ~ Has an even higher chance of capturing a Pokemon than a Great Ball
~Credit for information goes to Seribii.net~