Hi, I have a 2005 honda accord and I want to get bigger cooler rims but I'm afraid it might have some disadvantages on the car. What is the biggest size that I can use?

Yes, doing this on any car has implications. When you change rims or increase size, you are changing the weight of the rims. If you are going to up the size, you really should look into upgrading the brake system to handle the extra weight. Especially with a bigger rim. I LOL when I see hummers with 22's cause you can see the stock brakes right through the rim... good luck when you need to stop fast.

Check Tirerack.com they have a good system of pairing up rims to the car.

Good advice static FX, I found this out the hard way, I have a 1990 Mazda Miata (MX5) and I put a nice shiny set of 18" chromies on it... after I chewed through my brake pads at an alarming rate I upgraded my brakes!
You also need to get your speedo recalibrated as bigger wheels will put it out.