Obviously, the implications of a criminal record are dependent on the severity of the crimes you have committed---nobody treats a drug possession offence the same as a murder conviction. However there are certain consequences to having a criminal record that may affect your future regardless of the number or severity of the crimes you have committed. In some cases, these may continue to present themselves for decades.
Many convicts find that obtaining a job with a criminal record is very difficult. Many employers conduct criminal background checks before hiring employees because they can be held liable for harm caused by convicts in the workplace that could have been foreseen by a criminal background check. At the very least, a criminal record---for any crime---puts you at a disadvantage when you are competing for the same job against applicants who have clean records.
Rights as a citizen
Your rights as an American citizen may be limited if you possess a criminal record. The effect of a past criminal conviction on your right to vote depends on the state in which you reside. According to the Brennan Center for Justice, 5.3 million Americans are denied the right to vote as a result of a past felony conviction, and 35 states continue to disenfranchise past convicts. Serving in the military as a convict requires a special waiver, and certain offences (typically felonies) may excuse you from serving on juries.
A criminal record can have a severe impact on your search for housing since potential landlords---like anyone else---can conduct a background check. According to Human Rights Watch, "Exclusions from public housing are among the harshest of a range of punitive laws that burden people with criminal records." The likelihood of your being denied housing as a result of a criminal record depends on the nature of the crimes you have committed.
Not every criminal is equal under law. If you have a criminal record, you are far more likely to receive a harsher penalty by a jury, especially if you are committing the same crime again or if any of your offences have been of a violent nature.
A criminal record is not necessarily a permanent stigma. It is possible to expunge a crime from your record---the process of doing so will differ by state. An expungement does not technically erase your criminal record. According to FreeAdvice, "successful expungement will not erase the criminal record, but rather the finding of guilt will be changed to a dismissal"---this will allow you to say, when asked, that you have not been convicted of a crime.