The Airport Metro Express is a great option if you want to get into the city in under 20 minutes. Works well, is not crowded, and if you don't have much luggage it is easy to manage.
From the airport there are only 4 stops on the Airport Express - Aerocity, Dhaula Kuan, Shivaji Stadium and New Delhi station (NDLS).
Unfortunately, if you exit the Metro at Shivaji Stadium (closest for Connaught Place), it is not easy to find local transport to get you to the exact place you want to go.
There are auto-rickshaws, but they are a pretty grim bunch of guys who I don't trust much. It would be really, really nice if they had a pre-paid taxi service running from the Metro stations, to get you to your home or hotel or wherever else you want to go. I didn't see any, but maybe they do? Does anyone know?
But the Airport Metro Express does look like the perfect option for backpackers who want to get to New Delhi Railway Station. The budget hotels of Paharganj are very close to the station. The hotels also offer pickup from the railway station.
Here are photos from my Delhi Airport Metro Express trip:
Boarding from the airport. The train is not exceptionally busy.
A lot of airport staff are on the train, but also you see several people with backpacks and small suitcases.
Inside the Metro Express. Note the luggage racks.
Most of the journey is underground, but for some phases the train emerges outside and you can see the city below.
I loved this photo of the Green Bus and the Green Auto :) both running on natural gas. Delhi looks very green in this photo!
And in this photo too! This is the Delhi Ridge, the green cover that protects the city!
On the horizon you can see Rashtrapati Bhavan (the President's House) and the centre of New Delhi.
In 18 minutes, I exited at Shivaji Stadium on Baba Kharak Singh Marg, near the city centre.
I didn't see any taxis or auto-rickshaws waiting outside. Maybe there is a service. If anyone knows, please tell me.