Tent, sleeping mat, sleeping bag, ... : I really like the EXPED brand for camping gear. All their stuff is very high quality; not cheap though. It's a European company but they have excellent US support. I own one of their tents and a sleeping mat (Downmat). The Downmat in particular is just incredible :).
If you want to spend less, I would go shopping at REI. Their house brand is reasonably priced for good quality (there's much cheaper stuff still on the market, but less reliable), the stores have knowledgeable and helpful staff, and they have an incredible no-questions-asked return policy if you find out you don't like the gear you originally bought.
Bring the repair kit for your bag/pad/tent in case of tears and leaks. Add some duct tape to your kit, too - duct tape holds the universe together :).
Any small headlamp. (I have a Petzl Tikka XP - I like it because you can switch between diffuse (wide) and focused (narrow) beam.) Carry spare batteries.
Stove : I've sold my fancy stoves and now just have a PocketRocket. Supersmall (nice if you go backpacking) and works just fine. PocketRocket + pot is more versatile than one of the integrated JetBoil setups for dehydrated food, and only a little bigger.
Cookwear : if you have $$ to spend, Titanium stuff is nice because it weighs nothing (again, good for backpacking). But it loses heat faster and it really is 2-3 times more expensive than regular steel (heavy!) or aluminum (decent compromise).
Water Filter : a good old filter is more reliable than the UV pens and whatnot if you're going to be camping by / drinking from streams.
Stuff sacks : make sure you have enough of these so you can wrap everything in a waterproof layer.
Ten Essentials : you know ... compass, first aid kit, sunblock, knife, ...
Water : I hate bladders so I use good old fashioned stainless steel or plastic bottles.
Clothing : enough layers to stay warm. Use materials that keep you warm even when they get wet, and that dry reasonably fast. No cotton or jeans. Quick-dry shirts, wool, ...
If you are motorcycle/car-camping rather than backpacking, you can afford some luxury extras. Especially if you're bringing a girl - make her comfortable. It'll pay off :).
A typical kit for me :
* Tent (Exped Venus II if sharing or if I want space ; MSR Hubba if it's just me and I'm going lightweight) + repair kit
* footprint for tent if I expect bad conditions
* Exped Downmat 9 (sleeping pad)
* REI Zephyr 15deg sleeping bag
* headlamp (Petzl Tikka XP) + set of spare batteries
* maps (in waterproof sleeve if they're not water-resistant)
* sun protection (e.g. sunglasses, sunblock)
* mosquito repellent (e.g. lotion, or mosquito coil)
* fire (e.g. lighter, waterproof matches, a little bit of fire starter)
* water filter (I have the basic MSR model, forget the name)
* Pocket Rocket stove + 1 canister of fuel (2 canisters for longer trips)
* aluminum pot with lid. Spork. Titanium cup. (Optional - bowl)
* Pocket knife (I think it's a gerber - spend slightly more than minimum for something that won't break)
* Optional hiking (e.g. trekking poles), snow (e.g. shovel, ice axe, ...), or climbing (harness, rock shoes, ...) gear if that's the purpose of the trip
* first aid kit, including blister protection, which I always seem to need on hikes
* Some cash for emergencies
* Rain protection : I have a Northface shell, a goretex hat (Outdoor Research Seattle Sombrero) which doubles as a sun hat, and generic Northface rainpants
* Entertainment : I usually bring a book and a notebook, even when backpacking. If you're camping with friends, bring a board game.
* camp shoes (nothing is as nice as getting out of your hiking boots or riding boots at the end of the day! If it's summer, I bring my sandals as camp shoes)
* if hiking, hiking boots
* If I could afford the space, I would totally bring a foldable camp chair. Don't buy these online without testing them in-store first - some are terribly uncomfortable
* Clothing : layers! Make sure you'll be warm and comfy in the evenings. Put everything in waterproof bags. Don't bring too much; use laundromats on the way instead. Smartwool socks are the best thing in the universe.
* extra plastic bags (trash bags are strong and reliable). duct tape. some rope. A waterproof little bag for cell phone and wallet.
That should get you started :). If you have the option, start by borrowing stuff from friends. You'll quickly find out what you like.