I use the Mothercare black courier-style one. It's very useful with lots of pockets and a changing mat, but to be honest, the reason why I bought it is that DH is happy to use it too! Most of the others he wouldn't be seen dead with, and I didn't want to give him an excuse to get out of it. [whispers - DH is actually very good with DD, just didn't want to look like a wuss]
I don't bother with one, tiny handbag, a nappy, a plastic bag to put the nappy in (we use real nappies) a rolled up liner for wiping. There is normally water whereever you are and also changing facilities. It's not the end of the world to have to change a nappy on a cleanish floor.
I have two nappy bags. They are far too big. You can get a sleepsuit and changing stuff in a normal bag.
Bmama - yes it does have a shoulder strap but I haven't needed to use it. Have been using it for 5.5 months and is big enough for the twins stuff and still looks brand new. Have also been asked whether it was a changing bag or not - which is a bonus.
skip hop is great- it depends of what sort of person you are whether you get tiny bag/ massive one- i would say do get a bag big enough to put plenty of stuff in if you lke to be ready for all eventualities- nappy changes /puking over clothes- spare toys/ pants for toddlers.for me i think it makes life less stressful.
Really would go for a bag YOU like that's a sensible size, then go for a small foldable changing mat. TBH you are going to be carrying a bag for your LO for a few years, so think of yourself and what you are happy to carry.
You might not think you need a big bag when you have a newborn but wait until it's weaned and you are out for the whole day...try carrying two bottles of milk, a meal, some snacks, some water, a few nappies, wipes, bags to put dirty nappies in, a change of clothes, some muslin clothes, a couple of toys, your own stuff like purse, mobile phone, dark glasses etc....
Get something ergonomically friendly - eg that doesn't give you back ache!