My greatest weakness....

[AFK]

"My greatest weakness is delegation" is a good one to go for.  Anything that actually sounds fairly awesome when you think about it for five seconds is always a winner.

I've used that one a couple of times too. 

[Rumckle]

"Sometimes I wake up in pools of other peoples blood, with total amnesia."

?

I'm not sure I've actually been asked that in an interview before. I have had my references asked that however.

[LMNO]

"The inability to stomach answering pop-psychology business management questions like that one."

[AFK]

For me, the strategy depends on the interviewer.  You can get a good sense of them quickly, if you're not too nervous.

If they're a fun-loving sort, a bit of lighthearted chatter goes a long way.
If they're more serious, they will respect thoughtful answers to their questions.
etc., etc.

The last job I interviewed for, which I didn't get, was quite a hoot.  I knew the two people interviewing me and had worked with them on past projects.  I thought that would give me an edge.  Except, what I handn't counted on was coming down with laryngitis the day before and completely losing my voice.  But, I went on with the show, and well, I didn't get the job.  Fuckers!

[AFK]

"I like to share puns with my co-workers."

"What, we're done already?"

[Bebek Sincap Ratatosk]

I generally go for something honest... like "I sometimes have trouble finishing a project after I get bored with it and I have to keep several reminders in my scheduling program to make sure it gets done."

That way its an obvious flaw, not a false humility kind of response and it appears that I have something in place to compensate for it. But I think "the best answer" probably depends on the kind of work and the interviewer.

[The Good Reverend Roger]

"My greatest weakness is my hatred of stupid questions like this."

"Lost time due to STD flare ups."

"My inability to not stare at the breasts of my female coworkers."

TGRR,
Channeling Redman.

[AFK]

Yeah, I can that I have no problems with that last one.

Well, my office neighbor is okay looking, and the only one under the age of 35, but otherwise, yikes!

[Shibboleet The Annihilator]

ON OCCASIONS I HAVE HORRIFIC BOUTS OF EXPLOSIVE DIARRHEA, FORCING ME TO SHIT IN TRASH CANS BECAUSE I AM UNABLE TO MAKE IT TO THE RESTROOM IN TIME.

I SHOULD REMIND YOU THAT THIS IS A MEDICAL CONDITION AND IT IS ILLEGAL TO DISCRIMINATE AGAINST MEDICAL CONDITIONS.

WHEN CAN I START?

-StD,
recommends that you speak in capslock.

[AFK]

Interestingly enough, if I get this job I'd be working for the big hospital in my city.  I wonder if they give discounts? 

[Bebek Sincap Ratatosk]

Interestingly enough, if I get this job I'd be working for the big hospital in my city.  I wonder if they give discounts? 

What would you be doing?

[Requia ☣]

I usually pick something they already know by that point in the interview, my first job it was 'lack of experience' and my second it was 'face to face communication'.

[AFK]

Interestingly enough, if I get this job I'd be working for the big hospital in my city.  I wonder if they give discounts? 

What would you be doing?

Coordinating the substance abuse prevention initiatives in my city's schools.   

[Bebek Sincap Ratatosk]

Interestingly enough, if I get this job I'd be working for the big hospital in my city.  I wonder if they give discounts? 

What would you be doing?

Coordinating the substance abuse prevention initiatives in my city's schools.   

Cool, thats awesome that its based out of a hospital!

[AFK]

Yep.  The same hospital that my little boy will be born in.  Again, I'm hoping they offer generous employee discounts.