Anyone who has flown into Suvarnabhumi the past two years and taken a taxi into Bangkok will have noticed the construction of an elevated rail line from the airport into town. I noticed during my recent trip that they were installing the overhead electrical cables on the tracks, and that the stations looked close to completion.

The main terminal for this new high speed line will be Makkasan, located between Soi Asoke and the Plaza Entertainment building. This means taxi rides will be very short to most hotels for those who ride the train in.

You can read about it here. Expected opening date of May, 2009: http://en.wikipedia.org/wiki/Suvarnabhumi_Airport_Link

Rode the express a couple times on this trip. They are still getting things geared up but its running. Cost is 100 Baht for express to Makkasan. If you're staying near Soi Cowboy take a cab (50B) to Makkasan and ride from there. Nice comfy ride leaves every 30 min and takes about 15min or so to get to the airport.
Probably don't want to take a cab from there to your hotel as a right turn is about impossible from the station and it will be a LONG time for a taxi to get heading the right way. I walked to the Phetchaburi station and its one stop to Sukhumvit. Did get a quick bag search going in but nothing big.
You have the option of the city train and can ride all the way to Phaya Thai. If I were staying near Nana that might be a better option to grab a cab from that area.

link to airport express map
http://www.bts.co.th/en/Image%20Event/RouteMap_BTS%5Bok5%5D.gif

Soooo in another 5 years they "might" extend it to Pattaya??? Sure would be nice to pick up some phone numbers from the Thai girls that just dropped their sponsors off at the airport

I took the express train from the airport to makkasan station for the first time upon my arrival in bkk earlier this month. I arrived on the TG flight from LAX at about 6:30am with carry on bags (med size back pack and small duffel bag). Showed my TG business class boarding pass stub to get through fast track immigration and was able to board the 7:00am express train. In bkk at approx. 7:15 am. Walked outside the terminal towards the MRT station and caught a moto taxi to sukhumvit 22 for 60thb. was in my room by 7:30am. Because it was a weekday, I probably saved 15-20 minutes by avoiding the rush hour traffic (assuming I took a taxi). The cost was 150thb all-in (90 train and 60 moto). Normally I pay 300-400 for a taxi (I rarely take the tollway). I pick up the taxi on the arrivals level and negotiate a fare with them, some will use the meter (the 300 price) and others refuse and I end up at 400.

What javaj says in his comments about taxis not making a right turn out of makkasan is good advice. My moto could could barely make a right turn down asoke from makkasan. So a taxi would really struggle. Not to mention I didn’t see a single taxi waiting to pick people up. the walk to the MRT isn’t really that far but I’d stick to a taxi from the airport if I had heavy luggage. Or use a moto like I did if you have a light luggage load.

The TG flight bkk/lax also leaves one at the mercy of rush hour traffic with a 7:30pm departure time. So I’m planning to give the train a try on the return trip as well.