It depends on whether your interests match with the company you work for. If you are interested in being an Individual contributor for ever, many companies don't cut it - you will invariably switch to a managerial role after a few levels. So before asking this question, choose your company right.
Once you have the company right and the team right, you are usually setup for success. Also note, Career growth need not be the same as personal growth. And if you are chasing money, personal growth has an uncanny way of knocking out career growth at a later stage, IFF you grow enough. To explain, if you get really really good at X, even though you are at a low level career wise, soon you will see that there will be someone else who is ready to offer you a ton of money to do the same job, at their company. This also means you are well known for what you are good at: Make sure you collect trophies/patents/references along the way.
Having said all that, I can tell you what I personally try to do:
- Evaluate what kind of growth you are looking at - be true to yourself. Do you want to become the "guru" of X or do you want to become a great jack of all trades or do you want to rise as a great people / product / project manager. Each one of these will mean you focus on different things.
- Watch and learn everything the "smart" predecessors in your chosen career path in your team do. In addition to being awed by a fantastic piece of code / design, also question how they got there, and what were the options they evaluated. This is very crucial in growing as a person.
- Keep in touch with the outside industry and latest in your field.
- As Pierre pointed out above, ensure your networking skills are up to par. Even individual contributors are expected to be very good at social skills above certain levels. I have seen very few socially inept folks go very high. At the least, learn to listen.