Current WW1 sims (assuming you want to shoot at stuff and not simply fly around) roughly include the following big three: Rise of Flight, First Eagles and Over Flanders Fields...
Rise of Flight - the newest and shiniest of WW1 sims, it was released earlier this year, but it requires both a decent computer and an internet connection to play it (even when in an offline game), since it requests online confirmation that you have genuinely bought it in order to fire up every time you start it.
There has been some criticism that the campaign mode in it is a little lacklustre and that is true, but it is a pretty good 'dogfight simulator' for all that, assuming your computer is fast enough to run it without stuttering (and it will need to be). Unlike most other sims, you only get a limited number of aircraft with it, and have to buy other aircraft in order to 'unlock' them for use in the sim (they are about 7 quid each), but in fairness, that does tend to mean that the aircraft you do fly are genuine attempts at modeling the aircraft properly, so fidelity to the real craft is mostly very good (though not always). It is limited to fairly late in the war, so you'll be flying stuff like the Pfalz, Albatros DV, SE5a, SPAD, Camel etc. Do a search on 'Rise of Flight' in Google and you should find the website easily enough. You can buy it as an instant digital download (it's a big file though and takes a while to download) or you can buy it as a boxed DVD from various outlets.
First Eagles - With less pretty graphics than Rise of Flight, but still very good looking, First Eagles is a couple of years old. That means it is all 'patched up' and it runs well even on a fairly modest computer. There is an add-on 'mission disk' for it which expands the theatres and campaigns and adds more flyable aircraft too, so its scope is quite large, with many flyable aircraft, including all the usual suspects, with the notable exception of the Pfalz DIII, although that is supposedly on the way at some point as a freebie download.
There are many additional free aircraft which can be easily downloaded and added to it, and many people have created modifications for it which add additional campaigns, improved scenery, new weapons, improved flight modeling, famous ace paint jobs for the aircraft etc (look on
Home for those). This means it now covers the entire First World War period if you seek out such add ons.
It is based on a graphics engine which the developers (Third Wire) have used to make several flight sims, including Cold War and Vietnam War sims, but the graphics engine is definitely more suited to WW1 combat, since it only requires guns bombs and flak to be modeled, rather than radars, helicopters and missiles, which don't work quite so well in some of the other sims that use that engine. The flight modeling and combat is good fun and fairly realistic but not overly hard, and is scalable in terms of difficulty, so you can make it very hard, or introduce yourself gently to the thing. There is a version available which also includes the mission disk, and that means it offers good value nowadays. I would suggest this is a good introduction to things, since you can add a lot of stuff to it and make it harder and more complex if you like. It's fairly inexpensive too. Do a search on Google for either Third Wire, or First Eagles and you'll find it. It is available as a direct download, or as a boxed DVD.
Over Flanders Fields - OFF started out as a free add-on to Microsoft's Combat Flight Simulator 3, which came out in 2002. But having evolved into a very complex (and large) add-on, it is now sold as a DVD which you can install, so it is effectively no longer a freebie, as it used to be. To run it, you'd also need to buy a copy of Combat Flight Simulator 3, since it is still based on that sim and is effectively a 'supermod' of it, but this is not a major issue, as CFS3 is still widely available and usually to be found for less than a tenner. The OFF DVD however will cost you 20 quid. Even so, that compares favourably with the cost of Rise of Flight, and is not much more than First Eagles, which is the least expensive of the three.
OFF is massive in its scope, covering most of the air war of WW1, not the very early period, but from late 1915-ish onwards, so certainly most of the good stuff unless you crave flying in a BE2 and being shot at by a Taube or Eindecker in 1914.
Unlike either RoF or FE, OFF takes historically accuracy of the First World War very seriously, with a dynamically moving front line which matches the real war and all the aircraft flying their historically realistic missions from the bases they would really have been at in the real war, with realistic weather and such, so if you want historical accuracy, this is the one for you. You even have to fill out claim forms for your kills and name possible witnesses from your flight who might have seen it, so
Billy Bishop wouldn't like it LOL
The flight modeling and graphics are very good, however, even though it is based on a seven year old flight sim, because so much stuff has been added, you really need a decent newish computer to get the best out of it unless you are prepared to turn the graphical detail down, which you can do if you have to.
There are very few aircraft which you cannot fly in OFF and most squadrons and Jastas are in there too, with only the odd ones unavailable, and unlike with most other sims, that includes many bombers and recon aircraft too, as well as the fighters. A search for Over Flanders Fields will find it easily and you can buy the requisite copy of CFS3 it requires from places such as play.com and amazon.com
There are a few also rans, such as souped-up versions of Red Baron, plus others which use either freeware or older sim engines such as European Air War and Fighter Squadron. There are a few freeware ones kicking about too, such as 'Down in Flames'. Third Wire have announced they will be making a sequel to First Eagles as well, although that's a long way off appearing, and both OFF and RoF regularly add new content.
If you are more interested in realistic flight characteristics than shooting at stuff, you could also consider Microsoft's Flight Simulator X (FSX), which has a good few add on WW1 aircraft available for it, but you should bear in mind that you would effectively be simulating flying a WW1 craft in modern times, with no combat elements, so that might not be what you are after. But if it is, I would recommend taking a look on avsim.com, which is the internet mecca for flight sim fans.
You'll need a decent joystick to get the best out of a combat flight sim, and you should endeavour to buy one that has a throttle and a twist rudder function, since you're going to have to throw your virtual aeroplane about a lot. If money is no object, you might also want to check out Track-IR, which is an infra red sensor that attaches to the top of your monitor and detects your head movements and automatically pans the cockpit view for you, which is useful with dogfighting flight sims, since you have to look around a lot. But at a push you can get by with a hat switch on your joystick to shift the views around, so look out for a joystick that has one of those too.
Hope that helps a bit.
Al