how good of a credit score do I need to be a co-signer?

It needs to be good enough  to gualify for the credit card yourself.

Remember if she doesn't pay you are stuck paying

Do not cosign.  If she wants a credit card, get a secured credit card for her which is secured by an amount deposited in savings in the same bank or S&L and that is the limit of the credit card.  If you do not have money to put in savings for a secured credit card then you should not have a credit card.  

Sounds like your score isn't much better than hers.  If she needs a co-signer, he/she needs to have a score much higher than yours.  I would never co-sign for anyone.  If some can't pay their bills, why would you trust them enough to co-sign for them?

Don't do it. It makes you equally liable for her bill if she doesn't pay it.  If she can't get a credit card on her own, she shouldn't have one.  She'll have to start out with a secured card.

Nope, not good enough, and based on your other questions I doubt your score is anywhere close to the 600s.

Don't do it. If she can't get a credit card on her own merits, she shouldn't have a credit card.

While I fully agree with Scatty's response, at 620 you are almost certain to be turned down as a co-signer, so the question becomes moot.

Do you want to be responsible for all your girlfriend's debt?

Do NOT cosign for anyone!! Repeat not cosign for anyone. Much less your latest girlfriend.

Why? Your gf needs a cosigner because she can't be trusted to make the payments herself. Red flag number one.

Let's say you cosign. She gets the card maxes it out and can't or won't pay. Who is the card company going to chase next? Yep. You.

You refuse to pay and you end up with bad credit for some one else's debt. Red flag number two.

Then let's say you split up later this year. She still has the credit card. You are still the cosigner.... Huge red flag. Please don't be so naive as to say 'oh, we won't split up'. People who have been together 30 years split up. Never mind two youngsters....

You need to tell your girlfriend that there are credit cards out there designed for people with no or bad credit.... She needs to get one of those instead of relying on a cosigner!

UPDATE

my dad co-signs for my mom all the time, what's the difference? ..... The difference is that they are mature adults who are married. You are not.

We are going to get married someday and when that happens we will combine finances ..... Ok, and, if and when that happens, you can cosign. Until then gf gets a card on her own.