For a full list of all 130 countries and their current ranklings, please click here. The ranking and seeding system is complicated, but at present Spain has No. 1 ranking with the Czech Republic in second place.
This list of events for which you can buy tickets will show you which countries are so far scheduled to take part in the 2013 tournament. The ticket website also has a representative who is available on line, so you could ask direct questions about all the countries taking part and the dates.
The Davis Cup is now 112 years old. It started just as a competition between the USA and Britain, was expanded to include certain Commonwealth countries and now includes around 130 countries each year.