well there are tons to name, but i would suggest going to an anime website such as watchanimeon.com or something and select random animes. when u choose an anime it will give you a description of the show and tell you what genre/s it is/has. so you can go to the anime list and look through them alphabetically or when you choose a series and you see what the genres of the show are you can click on one of the genre and it'll show you all the anime with that specific genre. so if you are just looking to find some new anime to watch and you don't particularly care about the genre or whatever cuz you just love anime then i think doing it this way should lead you to some good ones. its what i do cuz i don't know what to watch and yeah if u just start searching/looking around on anime websites you'll find something good because--at least i feel this way--most of if not all anime is just awesome!
BUT some specific anime to start with could be things like: Full Metal Alchemist, the above suggestion of Neon Genesis Evangelion, Rurouni Kenshin is good, Darker than Black, Samurai 7 and Basilisk are really good... go from there and like i said just search around and i gaurantee u'll find something u like
