First, realize that "China" and "countries" as we know them are modern concepts. China was a feudal society where one king or warlord would build up his power and create an empire that would last a few years, decades, or centuries before it would collapse and be taken over by either chaos or another warlord. Sometimes not all of the previous empire's land would make it into the new empire and it would become a new group to contend with.
That said, my knowledge of China is limited to her historical interactions with the Koreans. During the Korean Three Kingdoms period, Goguryeo controlled what is present day North Korea and Manchuria. The Goguryeo allied with the Wei faction during the Chinese Three Kingdoms Period to defeat the Lioadong. After they did that, the alliance fell apart and the Wei and Goguryeo were at war. During the 6th and 7th centuries, they fought with the Sui and Tang dynasties. The Silla kingdom entered into an alliance with the Tang in an effort to defeat Goguryeo and unify the peninsula (under the unified Silla or Tang, depending on if you're Korean or Chinese).
This sort of stuff goes on throughout all of history in Northeast Asia, all the way to the Korean War. BUT, can we say that "China has a history of invading their neighbors?" Probably not. The Koreans frequently invited the Chinese in as allies and/or pawns to defeat internal enemies, and the definition of "country" would be hard to pin down. Manchuria traded hands numerous times between the Koreans, the Chinese, the Mongolians, and the locals, just to name a few. To whom does Manchuria "belong"? Why don't we say that China itself is being occupied by those rebels in the Communist Party and that the Chinese government is in exile in Taipei?
TLDR - The Chinese empires have frequently been active in their neighbors affairs, both by their own motivation and by invitation. We probably cannot claim that they are any more or less "threatening" historically than any other country.
A bit late, but I haven't seen any complete answers yet so I'll try and help you out. As a fore-note I'll use the term 'China' here to refer to the historical dynasties of the region, the modern concept of China is somewhat different but I do so for conveniences sake.
The attitude of China to its neighbours [and vice versa] varied substantially from dynasty to dynasty. Dynasties such as the Tang and Yuan had a domineering attitude to their neighbours - the Tang, for example, saw Korea as a "natural extension" of their empire - a 'tail' of China which must be conquered.
Equal sentiment was harboured towards the kingdoms of what constitutes modern day Vietnam, but the effectiveness of these policies also shifted with time. At times regions such as these were conquered and occupied by the Chinese, they would then rebel and be suppressed or freed of their occupation, at times factional disputes or other external threats would reduce Chinese influence substantially enough that they became de facto independent once more. At times the Chinese were simply outmatched on the field of battle and subjected to humiliation.
Other times they were tributary states - providing manpower, goods and money to China in exchange for somewhat nominal independence and protection from outsiders. And other times still alliances were forged and co-operation versus external threats was the name of the game.
It is important to note that Chinese dynasties after the Tang (618-907) showed little interest in expanding their territories historically outside of what they considered "all under heaven" which realistically constituted Manchuria, 'core China' in the North and South, outer Mongolia, Northern Vietnam, Tibet and sometimes Xinjiang, also known as 'Chinese Turkestan', and Korea. Even of itself relations with Korean kingdoms throughout history were complicated and mixed. You would however be more likely to find historical grievances in such regions, certainly in the case of areas such as Tibet. Conversely, until the 1960s Chinese militaristic involvement in, say, India was limited to several Mongol Yuan raids and a small-scale punitive Tang invasion of Bengal - throughout the entirety of Chinese history up to that point.
Adding more confusion to the mix is the concept of tributary status itself - whilst at peaks in dynastic power in Chinese history an abundance of Asian kingdoms offered to or were forcefully/diplomatically coerced into paying tribute to Chinese states, regularly throughout history Chinese dynasties weakened through various developments would essentially pay tribute to external powers themselves [largely steppe tribes] - the Chinese themselves did not see this as tribute but it's hard to objectively argue otherwise.
For the large part historical Chinese relations with empires of central Asia and the middle East were cordial, with empires such as that of Timur seen much more as potential allies and partners rather than targets of any conquest. As far as I am aware the Tang were the last who quarelled with such powers to any signifiance. Additionally China at no point fought a war of aggression with Japan, only having been on the receiving end - as a defender in both the Japanese invasions of Korea in the 1600s and the invasion of Manchuria in the 1930s.
Thus it is difficult to pin down an overall attitude towards China throughout history - for example whilst the Tang and Yuan were domineering, the Song acted often through diplomatic means and stressed coexistence [largely out of necessity]. Some countries were occupied by the Chinese at times and then allies at other times. Thus to many in the region attitudes towards China would be much more focused on modern history and recent developments which are outside the scope of the subreddit. It is undeniable however that, albeit with some stops along the way, Chinese dynasties - from the Han to the Tang to the early Qing and much inbetween - historically constituted the largest military, cultural and economic power in the region - and, until the 1800s - in the entire world. The image of China as a burgeoning world power has loomed largest for the longest amount of time, and has certainly influenced opinions of both the Chinese and its neighbours throughout time.
Sources:
China: A History - John Keay
The Age of Confucian Rule: The Song Transformation of China - Dieter Kuhn