If you've just bought your first DSLR camera then your bank balance might be looking a little lower than it did so please don't be tempted to rush out straight away and go mad on accessories. Photography can be an expensive hobby, and in the long run it's a good idea to spend some time thinking about what extra kit you will actually get the most use from.
Oddly, DSLRs manufacturers all seem to bundle their cameras with one or two lenses, but none of them as far as I'm aware include a memory card. So, seems as it's going to be impossible to take any photographs without one, your first accessory will need to be a memory card. The price of these are falling all the time, which can only be a good thing in my book. 1gb cards are available for less than 10/$20. If you've bought a DSLR then you're likely to have a 10megapixel (or above) model, so keep in mind that these will produce images with a fairly large file size. You might want to invest in several memory cards. I can't comment on models of DSLR that I don't use, but, with my 10.2megapixel Sony Alpha I get about 270 images in RAW format on a 4gb card (about 900 in fine JPEG format). If you google 'compact flash' or 'memory cards' then you get lots of retailers of memory cards to have a look at, so shop around for the best prices.
A good quality camera bag is an excellent early choice of accessory. Most DSLRs are fairly sturdy constructions, and will withstand some knocks, but a decent padded bag not only protects your camera, but also other accessories (and the larger ones will have room for other important things like your packed lunch). The range of camera bags and cases available is huge, and it can be very difficult to pick out the best one for your needs. However, even the smallest bags/cases will usually have room for your camera and an extra lens. My advice would be, if you can, to go to a retailer and take a look at what's available (even if you don't eventually buy from there). Check out how much padding and protection is offered by different bags/cases, how much stuff you can fit in, and whether they are comfortable to carry.
Most DSLR cameras come bundled with a lens or two these days, so you probably won't need to purchase additional lenses straight away, unless you have a very definite idea about the kind of photographs you are going to be taking. It's very easy to flick through the latest magazines and be seduced by the glossy pictures of new lenses. There are literally dozens available for most makes of DSLR, some of which will cost more than your camera did! Spend some time getting to know your camera and bundled lenses, as this will give you a better idea about the kind of photographs you want to take, before spending hundreds on any new lenses. If you find that landscapes are your thing then look at wide angle lenses (short focal lengths). If wildlife/nature photography is your thing then look at telephoto and zoom lenses with longer focal lengths (be warned, though, that top of the range telephoto and zoom lenses can be VERY expensive). Also consider lenses with macro (or close focussing) ability if you want to get up close and personal with your subject.
Lens filters are something to think about as your photography skills advance, and again the choice is vast, but, I would recommend UV/Protection filters as an early foray into the world of filters. These protect the front glass element of your lenses from dirt and scratches (better that your filter gets scratched than your 400/$800 lens) and can be left attached to your lenses all the time.
A spare battery should be a consideration. It's very annoying if you find yourself in the perfect location with perfect conditions to capture that perfect landscape only to find your battery goes dead. Also, if you're taking your camera on holiday, especially if you're travelling abroad, then it may be easier (and take up less space in your luggage) to pack a couple of extra batteries than to worry about what adapters and chargers you might need.
If you want to minimise camera shake or use long shutter speeds then a tripod is an essential piece of kit. Prices can be very high for a carbon fibre, top of the range model, so be certain you're going to use it before paying out for one of these. At the cheaper end of the scale there are some very good quality tripods available for less then 50/$100.
As you've probably realised, the choice and range of accessories available to the DSLR owner is vast, and can perhaps seem a little overwhelming (whole books could be devoted to the subject). I'll finish up with my top ten tips:
1: Once you've bought your DSLR and memory card (assuming you got at least one bundled lens) you don't actually 'NEED' anything else in order to get on with taking great photographs. So don't let any shop assistants try and tell you otherwise.
2: If you regularly buy a photography magazine then think about getting a subscription. It works out cheaper and they all offer free gifts (usually a useful camera bag). If it's a decent magazine then it will also help you learn how to get the best from your new camera.
3: Worth remembering are third party lens manufacturers (Sigma, Tokina and Tamron being the main three) who produce lenses for most of the popular DSLR systems at good prices and quality.
4: Check out amazon.com and look at the range of books/guides to photography that are available.
5: Think about what accessories you will actually use before you part with any of your hard earned cash. Don't shell out for a 500/$1000 lens if it's more likely to be sat in its case than on the front of your camera.
6: Make sure you've got enough memory available. Both in terms of your memory card/s and on your computer. If you take lots of photos (and you will) then additional memory cards and maybe an external hard drive for your computer will be good investments.
7: Get to know your own style of photography and the kind of pictures you like to take. This will answer many of your questions about what accessories to buy.
8: Always buy within your budget. Being able to pay your bills is much more important than a new lens for your DSLR.
9: The internet is your friend. Use it to research any new purchases before hand and find the best price. You can often use prices you've found on the internet to negotiate at your local camera retailer too.
10: Most importantly of all enjoy your photography.