Becoming successful in the corporate world depends on the particular company you are working for and career stage you are in at the moment.
For large and overly structured organizations, where lots of processes pre-determine your every step and all your colleagues generally have the same level of skills and get the same level of training, your success lies mostly in staying longer on the job, your discipline in following the steps, your alignment with corporate culture and, most importantly, your interpersonal skills - ability to deal with clients and colleagues and be liked by your boss. Often, pre-requisites for promotion are clearly defined. There is generally little flexibility and tools to get ahead faster and people are less important - they are cogs in "the machine". Additional technical skills, clearly superior to others may help get additional visibility at earlier career stages, ability to consistently meet your budget numbers will be important at senior levels.
In more entreprenerial organizations your personal impact may play much more important role. The best way to move forward here is to start thinking like the owner of the business. To succeed, you will have to understand the business and your role in it and do whatever necessary to move the business forward. Each your decision can be filtered by asking yourself if it will add value to the company. The bigger the impact, the more chances to get to the next level.
Finally, there are very unstructured organizations, some of which may be really large. Because there are no rules, structure or overarching idea, you generally don't know what needs to be done to get ahead, so your best guide here will be your boss and the boss of your boss. Make sure your boss looks good in front of his/her boss and you are likely to be considered an important member of the team. In such organizations personal loyalty and reliability is more important than anything else, because there is vertually nothing else your boss can rely upon to make things happen. At senior levels in such orhanizations corporate politics starts to play an important role. The person who accumulates the biggest power or, otherwise, ability to do things his/her own way, will get promoted, as this is often the only way to make something happen, when everyone have differing agendas and there are no rules to reconcile them. Ability to make things happen in such organization is considered a talent. It should be noted, that because of this, it can become the norm to fake such achievements, i.e. substitute beautiful powerpoint reports for real work done etc. This may temporary help, as auditing processes are broken as well, but may not be sustainable in the long run.
Clearly, these are extreme cases, and you are more likely to meet some combination of types, such as when work of regular employees is very structured, while senior managers enjoy absence of rules and engaged in lots of politics. In all situations, however, you will have to prove that you can do your own work well first, before you will be considered for promotion. Also, not all organizations are good for all people, some people will clearly prefer one type for another, so your best choice for promotion may lie in leaving your company to find another.
Career wise, starting work at the large structured organizations can also be a benefit, as you will see how complex things are being done and will be trained for free in many subjects other people will have to learn over many years. This alone might help you get much more senior position in another organization later.