Can someone who has entered the US illegally become legal resident?

If you are Mexican, 245i will help. Not sure about others.

245 I is the only way I know of that is legal.
I would be leary of anything else and make sure you confirm with a lawyer before proceeding.

Not true, 245i is not for Mexicans only. It is for everyone and there is a big question as to whether or not it will be re-introduced.

245i is only applicable if you have an employer, spouse, sister or whatever to sponsor you. If you don't have any means of being sponsored by anyone then 245i does not apply. 245i is not a green card or a work permit. It appears to me that many on this page believe that if 245i is re-introduced we will all get green cards -- not true.

deport illegal aliens

illegal aliens are criminals, not immigrants

A foreign national, currently out of status, and who has entered the country without inspection is removalable.

245i is a general amensty (similar to the 1986 law) that gives such persons a chance to adjust their status if they qualify. As a previous poster suggested, some kind of basis (sponsor) must exist.

If there isn't a sponsor, the removability issue must be overcome, which includes severe prongs such as "extreme hardship" to a close USC or LPR, a contracdictary condition in which the foreign national must proove that s/he has been here for over 10 yrs. without having violated any laws (labor laws included!).

So in short; yes in theory, it is possible for an unlawfull foreign national to adjust. But it's a very long process and practically not feasable (by the time 10+ yrs. are accumulated, the laws may change, for instance). Good luck!