India to Nepal: Delhi or Varanasi to Kathmandu:
It's quite easy, cheap, and an adventure to do this journey overland.
Take a train from Delhi to Gorakhpur. The Vaishali Express leaves Delhi at around 19:45 and arrives at Gorakhpur Junction at 09:10 next morning, or there's another train from New Delhi at 17:20 arriving Gorakhpur at 06:35 next morning. The fare is around Rs 2440 in AC1, RS 1240 in AC2, Rs 785 in AC3 or Rs 315 in Sleeper Class - see www.indianrail.gov.in for times and fares.
Take a bus or jeep from Gorakhpur to the Nepalese frontier at Bhairawi/Sunauli. Journey time about 2 or 3 hours, Rs 30.
Walk across the frontier, it's then a few minutes walk to the Sunauli bus station. Take a bus or jeep on to Kathmandu. Buses take 9 to 12 hours, cost about 120 Nepalese Rupees. There are many buses daily, either daytime buses leaving regularly until about 11:00 or overnight buses leaving regularly from about 16:00 until 19:00. If you have more information on travelling this route, please e-mail me.
It's also possible to travel via Varanasi. Direct buses from Varanasi to the Nepalese border at Sunauli take 9 hours and cost about Rs 100. No info about timetables is available.