First let me say up front - I'm not an attorney and nothing I say here should be construed or taken as legal advice. This is merely an expression, understanding and opinion of navigating US Immigration after spending years working through the US immigration system myself.
The immigration process is different for just about every method of immigration there is and each method of immigration has different qualifying criteria ranging from relatively easy to insanely difficult. The short answer to this question is - it depends on the method and circumstances of the involved parties trying to immigrate
First a quick listing of some of the most common methods of immigrating to the United States: Family Relationship - Marriage, Family Relationship - Non-Marriage (this would be like someone sponsoring a child), Work related, Immigration Lottery (Diversity Visa Program) and Asylum - Political, religious or otherwise (protection by the US Government). There are others to be sure but these by far constitute the largest applicant groups.
In brief: all family relationships (marriage or non) require a related sponsor that is either a US Citizen or Legal Permanent Resident (LPR). Work related immigration requires a business related sponsor. The Immigration Lottery which anyone can apply for (providing they're citizens of a qualifying country and have no mitigating immigration factors). Asylum, which anyone can apply for providing they can prove one (or more) of a variety of threatening persecutions in their home country.
More often than not, the two most substantial factors in determining whether or not legal representation should be retained when immigrating are - 1.) Does either party to the immigration process (US citizen, LPR or alien have a criminal background anywhere in the world) and 2.) Has the applying alien already broke (any) immigration law (foreign or domestic). As ICE (Immigration and Customs Enforcement) performs extensive background checks on both the sponsor and the applicant this WILL come out in the investigation.
Please note, if you fall into either of the above two categories it's still entirely possible to immigrate but the process will be much longer and much more complex than a standard filing where the parties involved are "clean" (no criminal history of any kind, anywhere). If you do fall into one of those categories it's probably in your best interest to obtain legal counsel. Omissions in the filing, improper filing of the forms and inconsistencies will almost ensure a denial and doing it right the first time without ever having navigated the immigration system is incredibly difficult at best. Can you still do it without legal counsel? Yes, but the odds are stacked against your success.
If the petitioner (US citizen or LPR) and the applicant are both "clean" the family immigration process is relatively straight forward and well documented (though lengthy). This has allowed for many people to successfully file and navigate this process without legal assistance. US Immigration is a fickle beast though.
They are notorious for suspending applications and issuing RFE's (Requests for Evidence) at even the slightest mistake, omission or unclear statement resulting in delays that can stretch months and in some cases even years. This makes filing the forms and adhering to their rules and processes vitally important. Accuracy, completion of required paperwork and clarity of information provided are paramount in ensuring a timely and successful filing. For this reason alone many people opt to engage legal counsel - though again, it's not necessary.
When filing as a business on behalf of an alien applicant it can be just as complex as individual filing if not more so. As this process is usually performed by HR management or staff who have little or no experience in completing the immigration process - many companies opt for legal help. As stated for individual filing, even small mistakes can add up to huge delays. For a company trying to obtain specialized labor to meet a specific need this can have a negative impact on business. Like the individual, you can go it alone but legal counsel should increase the odds of success.
Asylum cases are very difficult to navigate without legal help. This is one category where unless your situation is a high profile global or political event, successfully obtaining Asylum can be exceedingly difficult. A significantly high demand will be placed on proving persecution. Like all the others you can go it alone but the best way to stack the odds in your favor are through legal counsel.
Along with this topic of discussion, I think it should also be said that obtaining legal counsel is not a guarantee either. They're human. They make mistakes, and just like you - their mistakes can just as easily cause an application denial or very lengthy delay. In addition, not all attorneys are trained or specialized in immigration law so if you seek legal advice be sure the attorney your talking to has a demonstrated immigration background. While there are some good "general" attorneys out there that work with immigration - I personally would only deal with one who does immigration and nothing else (just my personal opinion).
I'd also like to remind everyone that it is a sad fact that there is a large group of fraud and scam artists out there preying on the vulnerability and hopes of both US petitioners and foreign alien applicants alike. Do your research, trust me - this is one part of your life you want to take your time and do things right the first time.
Beware of people who offer to just file your forms for you. More often than not they have no legal background at all and have no legal ground to represent you should you be pulled into court. In addition, you have little or no recourse should you engage one of these services and they misrepresent you resulting in a denial (or worse, disbarment) and it happens all the time.
Also, understand that Immigration is a Federal matter and as such - when seeking legal counsel you do not have to hire someone from within your state. Don't be afraid to ask the person or service you're wanting to represent you to provide their credentials (attorney's license verification). Ask them how many cases they've represented, what type they are (personal, business, etc.) and how many they've won and lost. If they're reluctant to answer, walk away.
Though I know it's not what many people want to hear, at the end of the day if your case has any mitigating factors you probably should seek legal counsel. I know Legal counsel is expensive. Just remember, like most things in life - you get what you pay for.
If you think you can go it alone, the best place to start is to download the instructions and forms required for your immigration circumstance and simply read through them. Believe me, you'll quickly get a feel for whether it's something you think you're capable of doing yourself not.
Finally - If you have a loved one or friend outside the United States that you're considering visiting and you've never traveled internationally before - you might want some additional insight into: