Hey, I'm sorry for not replying for a while... I could have sworn I did yesterday, but I guess I forgot to press 'Post Message' xD
Thank you all for the replies and the help!
I never expected this would be such a hot topic

You've all posted some really interesting suggestions, and I'd love to give you some direct feedback on which ones seem to work for me, but unfortunately I've managed to break a little of the code in the program I'm working on, which needs to be fixed before I can continue :/
It shouldn't take long though, when I can I'll play around with all your suggestions and let you know the result!
Chris has a good point, I probably didn't describe very well what I was after here, sorry about that. The game I am working on is a simulation of a game where (basically) you bowl metal balls at another ball, and try to get them as close as you can... Best description I can think of xP
It's called 'Boules' by the way, in case you're interested :3
In the image I posted earlier in the thread, the ball was wooden, but that's just an early placeholder. Real-life boules are metal with a number of grooves marked in them to show who they belong to in the game. Here's a picture of one, taken from Wikipedia:
My plan was to create a metal image to wrap around the sphere, then use Parallax Mapping to give the illusion of scores in the ball...
So basically I'm not just looking to hide the missing parts of the texture at the poles that make it look distorted, I'm looking to get rid of the texture pinching, and find a way to wrap the image smoothly around. Something like the image in Stab In The Dark's second post, or in Chafari's next post after that looks like the kind of thing I'm after

It's possible I'm not going about this the right way... Maybe I should try actually modelling in grooves in Blender, but my knowledge of Blender isn't exactly amazing

Thanks for offering to help me with Blender, Chris, it's a really kind offer, but you'd probably find teaching me anything pretty stressful xD
If I stop being lazy and put some effort in, I could probably figure it myself... Hopefully

Thanks for all the help