Lucytron, if you're still finding bloody veins even when your thermometer says you should be OK, check 2 things. First, are you sure your thermometer is calibrated/accurate? An easy way to check is to stick it into a pot of boiling, distilled water. If it doesn't register 212°, then you've got an issue. You don't need to replace it so long as you remenber your correction factor.

The other thing is where you place the probe when you measure your chicken. Hitting a bone, or right next to it, will give you a false high reading, since they retain heat more than the flesh does. Be sure to position the probe into flesh only....it may take a couple of attempts to find a good spot,

Short of a having a thermometer, the clear juice test is the only one I know. The temp in the cavity is only an issue if you've got stuffing in the bird. Otherwise, the thigh is the place to check temps.

Buy an instant-read thermometer. If you're going to roast a lot of any kind of meat, they're invaluable, and they can be found for a relatively inexpensive price.

Here's a tip I picked up from Elise Bauer's Simply Recipes site. It has saved me lots of guessing when I'm somewhere without my thermometer. Here's the link:
http://simplyrecipes.com/recipes/the_finger_test_to_check_the_doneness_of_meat/

This is also a problem for me - I love roast chicken but have a hard time knowing when its done, despite owning 2 meat thermometers! Last week, my thermometer registered between 170-180 in various parts of the chicken, including the armpit, and I still found a bloody vein when I cut it all the way open.
How do I avoid this?

The method Greenstuff suggests is good but not perfect. It doesn't tell you what's happening in the cavity. But until you invest in a meat thermometer (and you need one) that technique, as described, is the way to go. Also look at the skin. Is it crisp? Does it look like something you would want to carve and eat?

When you've roasted a lot of them, you can just wiggle a leg and tell. Until then, make a small cut at the point that the thigh meets the body. When the juices are clear (not reddish), the chicken is done.