I consider myself not to be an alien movie fan but I actually surprised myself with what I have watched and actually enjoyed.
I loved the original Predator; an action packed movie where not only are the commandos fighting against one another, they're also combatting against those nasty aliens camouflaged in the jungle.
Signs (with Mel Gibson) is an unusual alien movie which sticks in my mind. It doesn't contain any SFX, or grandiose models of aliens or haunting music scores but what captured me was the emotionally charged moments between a family fighting to survive - I guess this movie brings out that raw parental emotion of doing absolutely anything and everything possible to protect your kids.
Independence Day is another classic which I've enjoyed over and over. This one does contain the spectacular SFX (of it's time). Great casting where there is a great interaction of characters.
I can't go past "a funny" alien movie and my top of the tops would have to be Men in Black (I love Tommy Lee Jones).
However, my go to alien movie is District 9. The aliens have already landed and assimilated into society. I loved the story, the way it was shot and has provided me with many laughs along the way. In addition to making me think about societal issues such as racism, apartheid and Government repression. These are all very real issues but integrated so cleverly into this black comedic alien invasion movie.
I like sci-fi and aliens, etc, but I haven't really seen an alien encounter movie that I really like. I love The X-Files: Fight the Future, and they do see an alien in it, but it is only on screen for a few seconds near the end of the movie.