I assume that by "alive", you are also meaning "mortal" and not ascended (since there are an uncounted number of those, with Morgan Le Fay and Oma Desala being notable ones). There are several Ancients that were alive and mortal during the course of the series, although most of them eventually died:
- Ayiana (SG-1 Season 6, Frozen): Preserved in a block of ice in Antarctica near the second Stargate found there. Had a disease very similar to one that the Priors of the Ori eventually unleashed, and eventually succumbed to it.
- Orlin (SG-1 Season 9, The Fourth Horseman, Part 2): A previously ascended Ancient (encountered before by SG-1), he descended in order to provide an antidote to the plague the Priors had unleashed. The strain of having all his ascended knowledge in a mortal body eventually resulted in him having brain damage and forgetting what he knew. Orlin is the only Ancient who is still alive by the end of both series, albeit as a shell of his former self.
- Myrddin (Merlin) (SG-1 Season 10, The Quest, Part 2): Although seen in holograms in several episodes prior, SG-1 eventually found Merlin in a stasis pod where he taught Daniel Jackson how to construct the Sangraal (an anti-Ori weapon). He eventually died of the strain on his body.
- A shipful of Ancients in stasis (SGA Season 2, Aurora): The Ancient warship Aurora is found where the crew are in stasis and live in a sort of virtual reality. Shepherd and McKay talk with them, but realize that even with stasis they have aged so much that they would die if removed. They discovered there was a Wraith impersonating an Ancient in the virtual reality and set the self-destruct on the ship in order to prevent information about a weakness to the Wraith from falling into their hands.*
- A shipful of Ancients subject to time-dilation (SGA Season 3, The Return Part 1 and Part 2): An Ancient ship traveling just under the speed of light for thousands of years experienced time dilation and, when they slowed down, were perfectly healthy and took over Atlantis. They are eventually killed when human replicators attack Atlantis.**
While it's certainly possible that there are other Ancients who are preserved through some sort of stasis or also chose to descend, there are no clues that they exist. If they do exist, it seems that they do not want to be found, or don't have the means to broadcast their presence. Indeed, all of the Ancients, aside from Myrddin, were found by accident (including Orlin the first time they met).
* Sadly, this plot point of the Wraith having a weakness was never revisited
** These Ancients were jerks and wanted nothing to do with the Atlantis expedition. They didn't even bother to tell the crew what their name for a "puddlejumper" was!