I recently bought myself a Cannon EOS Rebel T3 and it came with the EF-S 18-55 MM lens. It's a good lens but i'd like better. I'm kind of new to photography so what would be a decent lens to buy??

I say stick with that one for a while. The canon kit lens is a decent starter lens. You're looking at another $400 - $500 to get something better. Use that one for a while, find out what you do and don't like about it, and then start looking for a replacement. Until you know what you want from a lens - something you'll only find out by using what you got - its hard to suggest a replacement.

I have also recently bought a Canon Rebel T3 - well I just bought the body as I was upgrading from the Canon 400D - so I had the kit lens the same as you have got, plus two other lenses that I had bought for the old Canon. I have a Sigma 10 - 20 mm which is a wide angle which I mostly use for landscapes, and then I have the Sigma 18 -200mm which I use most of the time. A very adaptable lens, going from fairly close up, through to zoom.
However, you say that you are fairly new to photography and I would suggest that before you rush into spending on an extra lens, you find what aspects of photography really interest you and you wish to develop. It is the eye that finds this, not another lens.

I think both comments above are very wise, but I’m also aware of what a powerful urge “lens lust” can be. Having succumbed to it myself several times, I can lay my hand on my heart and say “buy cheap, get nasty”. I’m also pretty sure you’re going to have to find this one out for yourself. The next lens you buy is going to be the first one you trade in – at a loss and with little regret as to its optical performance.

Leaving aside third-party manufacturers like Sigma and Tamron that offer some alluring alternatives, Canon has a very easy to understand philosophy about its lenses: you can put any lens made by Canon in the last 30 years on your camera, but if you upgrade to a full-frame or 1 series, your EFS lenses will not fit. The difference between a $300 Canon lens and a $3000 Canon L lens with the same focal length is of course the quality of the output, which is ensured by far better optics, and the quality of build. Generally speaking, the faster (i.e., the more luminous) the lens, the pricier it’s going to be.

Third-party manufacturers usually – but not always – design their lenses to offer similar performance at less cost. However, you can’t get something for nothing. For example, the focal range will be the same as the Canon alternative, but the auto-focus motor will be louder and slower and the maximum aperture will be darker. Sometimes this isn’t important. For example, if you’re into landscape photography, the maximum aperture doesn’t really matter so much, as you’ll be using a tripod anyway. A case in point: the Korean manufacturer Samyang offers (relatively) cheap fish-eyes and wide-angle lenses. Build quality is acceptable; optical output is rather good, but they’re all manual focus lenses. As the viewfinder on the T3 is rather small, you will probably have to use the live view function.

As the other two contributors have wisely said, settle in and enjoy what you can do now before splashing out more money. With that said, your next lens purchase will probably be a zoom lens with a longer reach as your kit lens goes from (just) wide-angle to (just) portrait. Canon has some low-end telephoto lenses – the 18-135 and 18-200 mm – which are relatively cheap, but for a reason: they’re not very good. There is also the EFS 55-250, which is a third of the price of the other two, and can be charitably described as your kit lens on steroids. Better yet: a piece of junk.

You may want to explore wide-angle photography. I don’t know Sadhya’s Sigma, but I can guarantee the Canon EFS 10-22 mm as outstanding. Alternatively, if macro photography is your thing, the EFS 60 mm macro is a joy to use.

I suggest you resist the allure of cheapo Canon / third-party alternatives and rent a good Canon L once you’ve found what most appeals to you.

Two web resources for lens reviews:
www.dpreview.com - arguably the best web resource around for digital photography
www.the-digital-picture.com - a good, sound, if slightly biased, Canon reviewer

I agree with Sadhya, think very carefully about the type of photographs you want to take before buying a lens.

If you want to take landscapes, you'll want something with a short focal length, say around the 10-20mm mark.
If you want to take portraits you'll be looking more in the 50-80mm bracket.
For wildlife you'll probably want a longer lens 200-300mm maybe longer for birds and smaller creatures. You'll also want a USM motor - ditto for sports as you'll want something that can focus very quickly.
If you want to take photos in low-light conditions or if you want very arty shots with an indistinct background you'll want one with a wide aperture (between say 1.4 and 3.2).
For close up photography you'll want a dedicated macro lens, or my solution: extension tubes.

With so many lenses to get, its unfeasible that any but the richest photographer could go and get the lot in one hit. So think it through carefully, what your new lens should be able to achieve.

As for hiring an L lenses, I'm sure that's a great suggestion if you're a top earner, but speaking as a mere mortal the last thing I'd want to do is develop the I-wants for a lens that would be beyond my means anyway.

Don't listen to those cautious ninnies and moaning minnies. Deep down inside you know you NEED a new lens. Tell us how much money you've got and we'll spend every penny of it for you and give you a bank overdraft to boot! ;)