IDK about notary but in AZ you 'most likely' will be denied a real estate license with a felony conviction - and also for several types of misdemeanors. If you don't report to the DRE within 10 days of a conviction, they'll scrap your license even if it wasn't something you might have been denied for.
It can also depend on how long ago the conviction was and your record since then. 

I'm not sure Gary Frimann, CRS, GRI, SRES . I have a clean record but I think ND is a little more liberal with their rules for Notaries then they are with a RE Sales person. I also think they are more strict with Brokers than salespeople. I will have to call both offices tomorrow to find out for sure.

I live in The Republic of California like you Gary Frimann, CRS, GRI, SRES so same as you posted regarding CA.

 Real Estate License:

In Florida YES.   But as Nina Hollander, Broker said about her states of NC and SC, an applicant who has a criminal conviction will face intense scrutiny from the Florida DBPR and the FREC.

Equally important is when an active licensee is convicted of a crime (either felony or misdemeanor).   

You must report it to DBPR.   Failure to do so may cost you your license.  The below excerpt is from Section 455.227(1)(t) of the Florida Statutes 

(t) Failing to report in writing to the board or, if there is no board, to the department within 30 days after the licensee is convicted or found guilty of, or entered a plea of nolo contendere or guilty to, regardless of adjudication, a crime in any jurisdiction. A licensee must report a conviction, finding of guilt, plea, or adjudication entered before the effective date of this paragraph within 30 days after the effective date of this paragraph.

Notary?   That I do not know.  

Here in Montana, felons can become licensed real estate agents but the  Montana Board of Realty Regulation considers each application for licensure on a case-by-case basis.

I am not sure and I don't think I am going to do the research on these subjects.  I will read the others answers but I think I will try to avoid being convicted of a felony as my first choice.   and to go on the record I do think convicted felons should be denied certain liberties that others might enjoy.  

In Texas, obtaining a real estate license with a felony is possible, but it does depend on an assessment made by the Texas Real Estate Commission (TREC). TREC will determine the applicants honesty, trustworthiness, and integrity.

I have been retired for some time now and once knew the answer cold and now have not a clue. Alan May covered Illinois and if my memory serves me, there are restrictions in Florida. 

It is possible to get a license in both NC and SC if a felon... but it will require huge scrutiny from the real estate commissions and won't be an easy process. As for notaries... I have no clue. If you don't report a conviction to the real estate commissions at time of application or after that's a good way to lose your license.

In Illinois, you are not precluded from obtaining a real estate license simply by having a felony in your past... it depends on what type of felony.  The types that will rule out licensing would include • Conspiracy to defraud • Forgery • Embezzlement • Larceny • Extortion • Obtaining money under false pretenses • A felony involving a lack of moral turpitude (whatever the heck that means?). 

And not paying your IL state taxes (they don't seem to care about Federal taxes), or delinquency of child support payments can cause a suspension, or eventual loss of your license as well.

In Arizona, I think it depends on the crime, but it wouldn't necessarily prevent.

Given that I am in the State of California, as you are, you know the answer. 

No, but not reporting it is grounds for having license revoked.

It might, I am not sure. I know a misdemeanor would not however you would be examined for it. I know any ethical misstep is flagged & addressed (as you stated), should one have a law enforcement episode. I do know that they weigh, at times, if being a licensed agent connects to the crime stated. If so, it is an automatic NO LICENSE.

In Colorado, you cannot be a felon to obtain a real estate license.   Not sure about a notary license.

This is California, Felons have more rights than law abiding citizens!

When getting a real estate license, if you do not disclose any past criminal convictions and the FBI discovers it on your record, you will be banned from receiving one. Also, you must disclose immediately when charged with a criminal offense. Failing to do that results in a loss of license.

Keep in mind, you can be a felon (if disclosed) or murderer (until caught) and practice!

Yes for Illinois if your felony is with money fraud, fraud against fidicuaries.

I believe in Colorado if you are a felony, you loose your license.

GOOGLE ANSWER > Can a convicted felon get a real estate license in California? Yes, you still may be able to obtain a real estate license if you have a prior conviction. It's important to note that you must disclose all past and pending criminal activity to the DRE as part of your license application.

We have to report any arrests or convictions to the state, not sure which ones could cost us our license though.

Maryland does not automatically disqualify someone for a real estate license if they have been convicted of a felony or misdemeanor. They weigh each conviction on a case-by-case basis and give the applicant the right to appeal if the application is denied.