I'm curious how many and which tournaments are considered to be "international titles".

The following list is from Sensei's Library. Is it complete?

Fujitsu Cup (24 tournaments)
Asian TV Cup (25 tournaments)
Tong Yang Securities Cup (7 tournaments, as I don't count the first two, discontinued, won by Yang Jaeho and Seo Pong-su)
IBM Hayago Open Championship (3 tournaments, discontinued)
Samsung Cup (18 tournaments)
LG Cup (18 tournaments)
Ing Cup (7 tournaments)
Chunlan Cup (9 tournaments)
Toyota & Denso Cup (4 tournaments. Discontinued)
Zhonghuan Cup (3 tournaments. Discontinued)
BCcard Cup (4 tournament)
Bailing Cup (1 tournament)
Mlily Cup (1 tournament)

What determines whether a tournament is "international title" level?

Fujitsu Cup - discontinued

Asian TV Cup - Yes, but regarded as a minor tournament. not a open tournament and prize money is small.

Tong Yang Securities Cup - discontinued

IBM Hayago Open Championship - I even didn't know this tournament exist

Samsung Cup - Yes. One of the major tournaments.

LG Cup - Yes. One of the major tournaments.

Ing Cup - Yes. One of the major tournaments. Ing Cup is mainly regarded as the most important tournament like a Wimbledon Open in Tennis because prize money is big and only 1 tournament in 4 years like Olympic.

Chunlan Cup - Yes. One of the major tournaments.

Toyota & Denso Cup - discontinued.

Zhonghuan Cup - Yes, but regarded as a minor even more than Asian TV Cup. Chinese player don't participate this tournament because there are political issue with Taiwan.

BCcard Cup - Yes, but discontinued temporarily.

Bailing Cup - Yes. One of the major tournaments.

Mlily Cup - Yes. One of the major tournaments. newest intl tournament.

So..

1.Major intl titles(currently) - China host: Chunlan, Bailing, Mlily cup
Korea host: Samsung, LG cup
Japan host: nothing currently.
Taiwan host: Ing cup

2.And there is a team tournament called Nongshim cup. http://senseis.xmp.net/?NongshimCup

My english is so poor so consider it~

LG, Samsung, MLILY and Bailing Cup are open to professionals worldwide (there are open preliminaries). Ing and Chunlan Cup do not have similar qualifier events, but they are still very important. Asian TV Cup is limited to only 7 players. But traditionally it is regard as a big event by the Chinese (e.g. winning it is treated as winning a major international title, in terms of special rank promotion). As already mentioned, a number of other major tournaments are discontinued: Fujitsu, Toyota, BCCard, Tongyang Securities.

The GoGoD tournament database has around 75 international events. These include women's events and restricted-entry events but even so the SL list is not complete.

However, in my eyes a title event is one that actually accords a title (Kisei, Honinbo), so I wouldn't personally count the Samsung Cup as an international title.

Being open is always a good pointer to an event's status, but even there there are anomalies. As I recall the TEDA Cup was open for Chinese players but Japanese and Koreans were invitees. Even the Fujitsu has been invitation-only and most other similar events have used combinations of openness, seeding and sponsor's picks, with openness being an important criterion only in recent years.

Money must be a factor, but some highly paid events have been highly restricted. Then there's the problem of the money not being enough to attract top Japanese players.

The international criterion is useless, as certain countries have sometimes been excluded, but more often, in what is billed as an open event, the sponsor's country gets a lion's share of the main places, and the qualification events are open only domestically.

Even if we accept that, say, the Samsung Cup and LG Cup are now very close to genuinely open events, with decent prizes and PR, and some continuity, if player A wins the Samsung and player B wins the LG, how on earth do we decide who is better, A or B?

There is no overarching body to regulate the events, there are no level playing fields, there is no consistency, there is no hierarchy. There is no foreseeable hope of an event that will tell us who the world's best is.

Then there are the rankings. Even if the ranking list shows a 12-year-old Chinese kid at the top, how many of us outside China would still believe Yi Se-tol is actually the best player?

Is it even possible for amateurs from Europe to participate in those major torunaments and if yes how?

(Let's just imagine a certain amateur has Sai behind them so their strength is not in question.)

Yes, for some of them there are places reserved for Western nations, e.g. the Ing cup has one space for a European and another for an American and the player will typically be chosen by some qualification tournament in those areas. Chunlan cup has a similar thing, e.g. here's Csaba Mero of Hungary playing Iyama Yuta in round 1 a few years ago. Take a look at http://igokisen.web.fc2.com/news.html and you can find out for yourself. Fernando Aguilar 6d of Argentina famously beat 2 pros in the Toyota cup a while back before Lee Changho stopped his run.

So if a player from Europe wants to participate there they must first win a lot of tournaments here in Europe?

I believe there are open tournaments where anyone can join -- of course, they must be willing to pay for their own travel expenses, room and board, immigration visas, etc.

No, just 1, the qualification tournament (e.g. http://www.europeangodatabase.eu/EGD/To ... y=T100127B). Though to get invited to that you'd probably need a high solid ranking. So if you turned into a 9 dan overnight people wouldn't believe you until you played in some rated tournament and won to show it (well, coming 2nd in EGC would be fine too).