>>354
Maybe you're talking about 複合動詞? If so, this site explains them in great detail:
http://www.geocities.jp/niwasaburoo/26hukugoudousi.html
The article is part of an HTML version of 現代日本語文法概説, an unpublished tome on Japanese grammar. Apparently the book is for native Japanese speakers so it'll be too intricate to read through, but I think you can pick many more examples of 〜込む-ish verbs out of the page. You can find the list that looks like this:
aspect modifier: 出す, 続ける, あがる, やむ, etc.
direction: 出る, かける, 入れる, 下がる, etc.
degree emphasis: 果てる, 抜く, 尽くす, etc.
mutual action: 合う, 合わせる,
others: 過ぎる, 間違う, etc.
As for なってきた, the verb+て+verb form belongs to a different category from 複合動詞, and the attached verbs such as きた in your example is called 補助動詞. These are listed and explained here:
http://www.geocities.jp/niwasaburoo/27hojodousi.html