I think Henry Ellis and Peter Goldsbury make very good points in the sense that "self-defense" is how one could best describe aikido if somebody asked them to describe "aikido" in their native tongue or in layman's terms. I've seen "self-defense" used to describe aikido in various books and dojo websites; sometimes they use "self-protection" which has spiritual connotations. Pretty much any MA could be taught, or at least marketed, as a personal self-defense method, so nothing unusual about that. I personally see "self-defense" as a broad term with different applications depending on context: anything from western boxing and grappling systems, to CMA, to combatives and krav maga; even iaijutsu was adequate self-defense some place and at some point in history.
I personally don't have straight or simple response when people ask me what aikido is. Sometimes I say something like "umm, it's like judo, with throws and stuff, and some wrist locks, but without competitions (not true of all styles I know)". Doesn't sound very appealing I know.
Sometimes I say "arms-length grappling with sword attacks", to differentiate from the closer range grappling of judo and bjj, and to emphasize that the traditional aikido attacks come from sword/weapons culture. In fact technically speaking, Daito ryu and koryu jiujutsu aside, kogusoku (semi-armored grappling) is the closest thing I've seen to standard aikido fare. Maybe I should answer "aikido is like kogusoku but without skewering the attacker" Wait, what?