What TYPE of camera should I buy for my trip?

Tough one. Either way you should get the camera well before your trip so you know how to use it without having to think about it. many P&S cameras make great photos, but the zoom and the quality of the lens can be low.
Maybe a "bridge" camera is the answer - one that doesn't have interchangeable lenses but offers a good zoom, and allows you to control the aperture and or timing if you want to.
There are plenty of this sort around. The one I am familiar with is the Pentax X70, which offers you 24x zoom,12 MP and the ability to shoot video.
There are of course others from the other manufacturers too, but as I said I am not familiar with those.

If you want to get a DSLR then look for a small one and take maybe just two lenses with you - a wide-ish one like the standard kit lens (18-55) and maybe a 50-300 zoom. Again I am only familiar with Pentax - maybe the new K-x would suit your needs. It has the advantage of using AA batteries too.
You could also consider the new Olympus Pen, which is tiny.
Of course all this depends on how much you want to spend too.

Due to physical problems I have always been limited to point-and-shoots for their weight...sadly getting limited results, as well. Until I found the Canon G10. While not as compact as some cameras, it will still fit into a jacket pocket -- but I have been able to take some amazing shots with it. (examples from my tests: http://bit.ly/rgw-photog). Learn how to use its manual mode and you will really love the shots it produces ("auto-mode" shots come out well, too.) Yes, you will lack an option for different lenses that you have with DSLRs, but weight when traveling is always a big consideration. At 15mp and the quality of the lens it gives you more latitude than many p & s cameras.

Enjoy your trip!

I always use disposable cameras for travel. Have for years. No worries.

Consider that you'll have to carry that camera around all day.

If you're going to be backpacking where every extra ounce may start feeling like an extra pound at the end of the day, you may want to start with a nice little point and shoot.

You may want to look at Olympus' new digital PEN series of cameras. Here's a quote from their site (http://olympuscanada.com/cpg_section/cpg_digital_slr.asp?section=pen):

Not a Point & Shoot. Not an SLR ... It’s a PEN. In 1959, Olympus designed a camera with the photographic optics of an SLR and the size and simplicity of a point-and-shoot—revolutionizing the way we take pictures. After 50 years, the PEN is back. And it’s mightier than ever. Introducing the new Olympus PEN. It’s totally digital, and offers unique and groundbreaking technology to a whole new generation of camera users.

The PEN provides superior optics, interchangeable lenses and multimedia capabilities—and combines the creative freedom of a sophisticated digital SLR with the simple controls and small size of a point-and-shoot.

The camera uses the same size sensor as the Olympus DSLRs which is significantly larger than P&S cameras and will therefore give you better image quality. There are only two lenses available right now specifically for these new cameras, but you can use any of the Olympus SLR lenses with an adaptor.

Oh, and Panasonic also has cameras/lenses in the same format (which is called Micro Four Thirds). You can get more information on them here:

http://www.four-thirds.org/en/microft/body.html

The Panasonic micro four thirds is getting better reviews than the PEn it seems.
You still have quite bulky lenses with them, and tbh a small APSC DSLR with a super zoom is probably as easy to carry as those.

Canon have some interesting new "S" range cameras out with long zooms which may be of interest to you. http://tinyurl.com/p2hht

Avoid ultra small cameras and look for image stabilization -
unless you have a very steady hand or use a tripod you get lots of blurring, and a tripod defeats the purpose of a small lightweight camra.

I have a canon powershot SX200.
12x Optical Zoom lens and wide-angle lens (28-336 mm equivalent), and weighs 7.7oz
It has enough manual settings to feel like I'm exploring a new world, and takes great autofocus shots. Only problem for a backpacking trip is the proprietory battery, but if you have the ability to recharge every couple days or if you don't take hundreds of shots daily it should work great.

http://www.steves-digicams.com/camera-reviews/canon/powershot-sx200-is/canon-powershot-sx200-is-review.html

I should also say that Steves digicam is a great resource for camera reviews
http://www.steves-digicams.com/

another site to check for impartial reviews is
http://www.consumersearch.com/digital-camera-reviews

I just bought the new Canon S90 (you can find it for around 430 or so) and just love it. I bought it specifically for the times I didn't feel like lugging the DSLR and all my gear around. The DSLR goes on the trip with me, but the S90 comes out when I don't want to be weighed down. I wrote a thread on it, click on my name if you'd like to see it.

If I were backpacking around Europe again, I'd be inclined to just take the S90 unless I had planned to stay in hotels versus hostels (I personally would stay in hotels, but several years ago I did the hostel-trip). You don't want to have to secure an expensive camera every night or feel obliged to carry it around because you don't feel safe leaving it back at the hostel. A tiny camera will go with you everywhere without bother.

My office uses all Canon Powershots, they're great little cameras. I agree with others above I would not take a large or an expensive camera on a backpacking style trip. Too much hassle to secure and draws attention.

I agree with the others about going with a smaller camera too. Unless you're going someplace like wildlife viewing where you would need a bulky lens to zoom in on something small, there are so many options with P&S cameras nowadays. Image stabilization is key. If you can get one with video capabilities I personally feel that's a bonus. My little Canon Powershot that I've had now for three years takes better video than the 5 year old Sony camcorder, and is easier to download.

I wrote this earlier on another forum. I'll copy it here.

I've had the new Olympus PEN E-P2 for about 2 weeks now and it's the most exciting development in my photography life in over 25 years! http://www.dpreview.com/reviews/specs/Olympus/oly_ep2.asp

I switched from film (Canon SLRs) to digital in 2003. Since then I've had (still have, actually, as I never seem to be able to get rid of old or outgrown equipment I've grown fond of): 2 Nikon dSLRs and the wonderful, amazing Leica Digilux 3 dSLR. Great cameras all, especially the Leica, not only because it makes great pix with the characteristic Leica look but also because it works like an analog not a digital, with dials to turn and buttons to push rather than menues to search through.

But this new little Oly is WOW! It has a wonderful live-view finder, can take 6x6 square format, amazing monochrome with a real film look, and best of all it feels like my old (film) Canon AE-1 in the hand, my favorite camera of all time, solid and sturdy yet small, compact, light-weight and nimble. And it's half the size of my Leica (and my Leica is much smaller than my other dSLRs).

This guy, Kirk Tuck, says it better than I ever could, and captures that sense of being in love for the first time all over again, totally smitten and dancing on air: http://visualsciencelab.blogspot.com/2009_12_27_archive.html

I can't keep my hands off it, I'm shooting anything and everything just for the sheer pleasure of handling it, trying out old lenses with it. Gotta go now - there's a rainbow outside my window!

Forgot to mention, the Micro Four Thirds lenses from Olympus are amazing, small and light, but I can also use my wonderful Leica 2.8-3.5/14-50mm. Check it out!

For a lightweight and slightly smaller quality DSLR camera, have a look at the Lumix (Panasonic) G1 great DSLR ideal for travel.

Muck