This is probably one of the most asked (if not controversial) questions about the series. It is unfortunate that there are still many, many "LHOTP" fans who believe that Albert Ingalls did indeed die at the end of "Look Back To Yesterday". While it is still true that Albert did have a rare and potentially fatal blood disease, that certainly did not mean Albert died.
The answer to this question was right there on the screen. Viewers who chose to believe Albert is dead missed three key points:
a) In the closing narration of "Home Again", Laura Ingalls states that Albert returned to Walnut Grove years later and that the family was happy to see Dr. Albert Ingalls home again. Albert did return to the town in "Look Back To Yesterday", but he was already ill and not yet the doctor. But, both the closing narration and the final scene in "Look Back..." (which we'll talk about in a moment) implies that Albert would have had to successfully earn his Masters' degree in medicine and returned to Walnut Grove one final time (as the doctor) at some point after "Look Back...", but before the town was destroyed in "The Last Farewell" (which Albert did not appear in), so therefore his last visit was never deplicted in any subsequent episode beyond "Look Back...".
b) It is very clear to me (and I hope it is to you too) that Albert Ingalls LIVES through the final scene of "Look Back To Yesterday". The very last scene in "Look Back..." has Albert successfully climbing the mountain, finding the treasure, and holding his hands high in the air. There is NO depliction whatsoever of Albert's death or funeral. If Albert had indeed died, then the closing narration of "Home Again" would have been proven TOTALLY FALSE.
c) At the beginning of "The Last Farewell", Charles mentions that he and his wife had last visited Walnut Grove three years back (the film is set in 1901). Although Albert was never mentioned, this point more or less supports Laura's closing "Home Again" narration of Albert returning as the doctor.
The scriptwriters may or may not have meant for Albert to die in the show, but after discussing the three points about his fate, there is absolutely no dispute that the answer to this question is a clear and resounding NO.
You can also watch it on YouTube:
1/10: http://www.youtube.com/watch?v=f5lv63k_AE0&feature=related
2/10: http://www.youtube.com/watch?v=7B7zc5iIHgs&feature=related
3/10: http://www.youtube.com/watch?v=sItNd6cyPqQ&feature=related
4/10: http://www.youtube.com/watch?v=cHaUMtwuYqc&feature=related
5/10: http://www.youtube.com/watch?v=wTirge0M9QY&feature=related
6/10: http://www.youtube.com/watch?v=fevys_1cf2o&feature=related
7/10: http://www.youtube.com/watch?v=OjmtosiUb1Y&feature=related
8/10: http://www.youtube.com/watch?v=w35fnFC_e9A&feature=related
9/10: http://www.youtube.com/watch?v=9nZU9KWkRbA&feature=related
10/10: http://www.youtube.com/watch?v=IKVZSqBwGNQ&feature=related
Hope I helped!!!! :-D