- Step 1: Check your operating system of your phone first. Then download and install an exporting software that works with your phone:

• iPhone: iPhone-iSMS (free, .csv format), Missing Sync (.csv format), iSMSExporter (available from AppStore, .csv format, please uncheck "Use AddressBook")
  
• Nokia series/Symbian: Nokia PC Suite (free, .csv format)
• Window Mobile phone:  Window Mobile SMS Import (free, .xml format)
• BlackBerry: ipddump (free, .csv format), Missing Sync
• Sony Ericson: MyPhoneExplorer (free - export to .csv format)
  
• Other phone models: MOBILedit (this software support almost of phone models,export SMS into .xml format)
  

     Free one works with almost phone.

- Step 2: Export SMS from your phone with installed software.

- Step 3: Copy exported file to the SDCard of your Android Phone.

- Step 4: Open SMS Migrator, configure carefully parameters (especially Export Software  and Encoding that you had used during exporting process), and select your sms file on SDCard (don't forget to turn off USB storage for your SDcard on your Android phone). DONE

Step 1, 2 work on your old phone and PC (or Mac/Linux), step 3 works on your Android phone plugged on your PC, step 4 works with SMS Migrator on your Android Phone.

Notes
- If your phone is not supported by above software, drop me a few lines with the detail of your phone (such as phone model, OS, etc.)
- If you use other software to export your SMS, please contact me.

Android Market Problem:

- Google does not sell app for certain countries. Please checkout here http://market.android.com/support/bin/answer.py?hl=en&answer=143779
However, you can buy it on SlideME.org https://slideme.org/application/sms-migrator
- If you run on FroYo, please consider this article that may help you to show protected apps. http://forum.xda-developers.com/showthread.php?t=687371
- UK users: How to fix UK Android Market download and Gmail log-in errors