something like this should work
Code:
myanime=[]
for _ in range(10):
    newEntry = raw_input("Enter a new entry :")
    print "My Favourite anime: \n" + newEntry + "\n - "
    myanime.append(newEntry)
f= open("myanime.txt","a+")
for item in myanime:
    f.write("%s\n" % item)
f.close()
St.O