Thanks for your tips. Here are my observations:

• desoldering pump - After cleaning and oiling my pump I had still no luck with it. Maybe I have to practice more :)
• desoldering braid - Adding some fresh solder before using this definitely improves the cleaning effect, but it leaves the solder inside the hole. I've tried three different types of solder wick without success.
• tap-tap method - It seems usable for smaller boards but not for a computer motherboard so I have not tried it.
• Pushing out - I had no thin solid wire here, so I added a little extra solder and heated the via while pushing in the new capacitor from the opposite side. Sometimes worked but this thing has two legs and I have only 1 soldering iron :)
• Blowing out - I tried to blow with my mouth without any effect. Then I tried a dust blower, but I cannot aim it precisely into the hole.

Then I found something in my drawer:

It is a plastic bottle with metal needle head, 1 USD from DX. I inserted it to the hole from the opposite side then I heated the hole. After removing the soldering iron I quickly squeezed the bottle. It cleaned out the via! 8 of 10 times I was able to insert the new component to the hole without problem. For the remaining two holes I used a sewing needle to broaden the hole.

Still not he best method, but it worked for me better than any others mentioned here. However I am considering to buy a vacuum desoldering tool to save a whole day next time :)

Thanks for your tips. Here are my observations:

• desoldering pump - After cleaning and oiling my pump I had still no luck with it. Maybe I have to practice more :)
• desoldering braid - Adding some fresh solder before using this definitely improves the cleaning effect, but it leaves the solder inside the hole. I've tried three different types of solder wick without success.
• tap-tap method - It seems usable for smaller boards but not for a computer motherboard so I have not tried it.
• Pushing out - I had no thin solid wire here, so I added a little extra solder and heated the via while pushing in the new capacitor from the opposite side. Sometimes worked but this thing has two legs and I have only 1 soldering iron :)
• Blowing out - I tried to blow with my mouth without any effect. Then I tried a dust blower, but I cannot aim it precisely into the hole.

Then I found something in my drawer:

It is a plastic bottle with metal needle head, 1 USD from DX. I inserted it to the hole from the opposite side then I heated the hole. After removing the soldering iron I quickly squeezed the bottle. It cleaned out the via! 8 of 10 times I was able to insert the new component to the hole without problem. For the remaining two holes I used a sewing needle to broaden the hole.

Still not the best method, but it worked for me better than any others mentioned here. However I am considering to buy a vacuum desoldering tool to save a whole day next time :)