The only comment I ever get out of these is the "Your Japanese is very good." which of course I hear even if all I ever said was "Good morning." My standard response to that one is いや、そんなことないですよ。まだまだですよ。or similar. Or I will reply, especially to people younger than myself, 優しいですね。Another variation, slightly longer, would be 褒めてくれてありがとうございます。でも、そんなことはありません。まだまだ下手ですよ。 I think the whole "taboo" about just saying thank you is changing, or is a generational thing. When I say to young people (25 or under) a compliment like "That's a cute outfit." I often get a やった！response with a little fist pump, which in fairly close to "Yes!" in English.

There are lots of phrases you can use in this context if you wish to be humble. Japanese people often use phrases that are self-deprecating. It's not necessarily meant to sound as if they believe they are as small as they make themselves out to be, but it's a part of the language and therefore the culture. Here are some phrase you may often hear: いいえ、いいえ。 "no, no" そうではないですよ。 "It's not like that." These are just some general phrases, but Japanese people in more specific contexts may put themselves or their creations down in order to be polite. If you do accept a compliment, it's not a huge deal, as many Japanese people tend to forgive foreigners more easily, since it is assumed that foreigners do not necessarily understand these sorts of cultural norms. Do your best to do as the Japanese do, but you won't be held accountable for those mistakes unless it's obvious that you should know the customs and simply ignore them. I hope this helps! Let me know if you have other questions.

Saying just ありがとう is completely normal. Denying sounds like old manner. If you want to be very formal, you can say 「恐れ入りますosore irimasu(I'm afraid to hear that.)」or 「恐縮ですkyoushuku desu(same as above)」.

[moved my comment to the Answers section]

It is not uncommon to be modest in Japan(ese). So, if someone told that something is good, you might in some cases hear people deny it or act surprised.