A few ways to decide whether it's worth it:
Is it damaging or just embarrassing?
Some things that show up online are merely personal things that we'd rather have go away. Others can damage chances at jobs, career advancement, future income and relationships. If what you are seeing is not anything serious, it may be fine to let it go. But, if what is showing up online includes arrest records and jail photos, it can be worth the trouble to remove it from the front page of Google.
Is it costing you money not to do it?
If you suspect that your Google results are keeping you from getting a job or from advancing in your career, it may be worth it to seek professional reputation management. In some cases, a potential employer will tell you that you were passed over because of what they saw online. While reputation management can seem expensive, if it keeps you from earning money, the price can be worth it.
How to tell if professional reputation management is worth the price.
Check several different sources and see what services they provide. Try to find one that will give a no cost evaluation of what needs to be done, and what sort of results they can promise. Most use a combination of free apps and proprietary software to get results. Some providers also have free tools available. If they won't give a free analysis or straight forward answers about their services, consider another provider. Seek out the company that offers the cheapest prices while providing the best value.
If your online reputation is holding you back, get started now. It takes time to see results, and the sooner you begin, the sooner your life can go on.
It can be upsetting when links to things from your past that you'd rather forget intrude by showing up on the front page of Google. If you are looking at the page thinking, "is my company going to fire me over this? Will this damage my future?" some reputation management may be in order.