If you liked
Hayate no Gotoku!
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...then you might like
Astarotte no Omocha!
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Watching the first two episodes is enough to notice some similarities between Astarotte no Omocha! and Hayate no Gotoku! First physically, both (Nagi and Astarotte) are small-sized, blonde haired and green-eyed. After this, behaviors, both are a little bit selfish and distant at the start (Tsundere in other word). You'll also notice that both feel lonely in their vast realm (mansion in Nagi's case). To conclude on girls, both have Rie Kugimiya for voice actress. Hayate and Naoya are especially similar in behavior, they'll do anything to satisfy their little master, to summarize they are totally devoted. They are both involved in a world that they don't know. Hayate no Gotoku! is more focused on humor and anime/manga references.
If you liked
Zero no Tsukaima
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...then you might like
Hidan no Aria
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Zero no Tsukaima and Hidan no Aria are not similar in period but have others similarities like : Seiyuu Rie Kugimiya as a pink-haired tsundere, a devoted slave and to finish .. all other girls have huge breasts.
If you liked
Higashi no Eden
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...then you might like
Xi Avant
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The things that will probably make you remember Higashi no Eden in Xi Avant are cellphones. In both anime cellphones are able to recognize somebody via a social network ("Eden of the East" for HnE). Also both seems to take place in the same period.
If you liked
Seikimatsu Occult Gakuin
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...then you might like
Gosick
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Both are stories about mystery and strange things, both take place in a big Academy. Maya and Bunmei are also similar to Victorique and Kujou (The girl is higher than the boy)