Citizens of Armenia, Azerbaijan, Belarus, Georgia, Hong Kong SAR, Kyrgyzstan, Moldova, Mongolia, the Russian Federation, Tajikistan, Turkey, Uzbekistan, Ukraine and Serbia do not need visas to enter Kazakhstan.
Citizens of Australia, Austria, Belgium, Bulgaria, Canada, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malaysia, Malta, Monaco, Netherlands, New Zealand, Norway, Oman, Poland, Portugal, Romania, Saudi Arabia, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland, UAE, United Kingdom and USA (Jul 2009) can obtain single-entry (up to 30 days) or double-entry (up to 60 days) tourist visas without providing a letter of invitation.
Citizens of Australia, Austria, Belgium, Canada, Croatia, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Liechtenstein, Malaysia, Monaco, Netherlands, New Zealand, Norway, Poland, Portugal, Saudi Arabia, Singapore, Slovakia, South Korea, Spain, Sweden, Switzerland, UAE, United Kingdom and USA (Aug 2010) with valid Kyrgyz tourist visa can travel also to Almaty Oblast and Zhambyl Oblast of Kazakhstan. However if you have two-entry Kyrgyz visa and you cross the border from Kyrgyzstan to Kazakhstan, you can't return back on this visa to Kyrgyzstan. Most customs officers don't know about this agreement, which can cause long obstructions at border crossings.(Update Nov 2011. NO officials know of this agreement and you will be turned away with a stamp on your Kyrgyz visa that says no entry)
For more information you should contact a Kazakhstan diplomatic mission in your area or Kazakhstan MFA's website Ministry of Foreign Affairs of Kazakhstan. Note that as of June 2012 the Consulate General of Kazakhstan in New York says it only accepts money orders, but they actually accept cashier's checks as well.
Note: Although the