I didn't have anything but point-and-shoot experience. When I decided to take up photography as a hobby, I made a giant leap into the world of DSLR. If you're really wanting to "take up photography", I do recommend making the jump as well. Its confusing at first, but if you're willing to do the reading on using your DSLR, you will not be disappointed.
The biggest thing about DSLR cameras is that if you leave them on "auto" mode, they won't take photos that are much better than any other point-and-shoot on the market. You have to take that leap and push the dial to the little scary "M" (for Manual) and leave the point-and-click world of auto settings. It's not hard to find information on the 'net on what every feature and setting in Manual mode will do for you, and it is well worth learning for the beautiful results you will get quite quickly even for a beginner.
I have a Canon 550D T2i and even with just the kit lens, a camera like this has been a fantastic jump into the DSLR world.
The T1i / T2i (and T3i which is nothing but a T2i with a swivel screen and some other very minor changes all for a price jump.. it is, in my opinion, not worth the extra money) are considered "mid-level cameras" which might scare beginners away, but trust me when I say they are not hard to learn, and having a more mid-level camera gives you the opportunity to grow without having to buy a new body for quite awhile. If you wanted to save money in the DSLR line though, you could go down to the T3 (no "i"

) which is an entry-level camera.. however I'd still recommend saving the extra money and going for something a bit more, but that's just me.
I like the Canon line of cameras, I'm not a Nikon girl, but some people are tied to one brand or the other, and still there are additional brands on top of those (Canon and Nikon do tend to be the two major faces though). Just remember whatever brand you choose will be what you stick with, because the lenses between different brands are not interchangeable (there's an exception to this rule, where you can buy adaptors, but that's not important right now).
To save some money as well you can look into used cameras, preferably ones that are sold by stores who have professionally cleaned the units before re-selling them, but you can also find them on places like craigslist or kijiji -- however keep in mind when purchasing directly from another user, you never know quite what you're getting, and when you're a beginner who is already knew to the type of camera and who may not be able to test everything out to make sure it works appropriately, you may want to stick with new, or at least certified used from a store. There are some ebay stores that guarantee their used cameras as well.
And if you aren't really ready to take that camera off "Auto" mode and move into the realm of Manual settings, I strongly suggest you stick to the point-and-shoot camera world, which are generally much cheaper, and much more user-friendly for quick-setting basic photography.
When someone says they want to "get into photography" though, I assume they mean all-out "I wanna
learn". And if you wanna learn.. a DSLR is for you.
