I use Pond’s Cold Cream. Inexpensive, and a little goes a long way in my opinion.
I use this, and I am superallergic. It works great and it’s not expensive at all.
The Body Shop, Neutrogena, and Almay recs are all good ones given the OP’s critera.
P.S. Why are people recommending lotions and oils and cold cream when the OP said “non greasy?”
I guess it depends on your definition of “greasy”. Monoi (refined coconut) oil is an oil, but it definitely doesn’t leave your skin feeling “greasy”. I’ve only ever used cold cream on a few occasions. I simply don’t remember it feeling greasy, and I’m really pretty sensitive to anything that leaves a residue on my skin (which is why I rarely wear makeup, I just don’t like the way it feels). Maybe they’re different brand-by-brand? There’s a definite difference in the way good oils feel on (and affect) your skin versus “grease”.
I use Johnson & Johnson Baby Wash as a face wash in a pinch (it’s in the tub because I use it on the kids). It’s tearless and soapy, and is great at removing eye makeup. It costs about 4 bucks for 16 ounces.
I finished my bottle of Clinique blue stuff, and I also decided it was too expensive. I tried a bunch of others, including the Neutrogena and Almay, and wasted more money than I would have spent on a bottle of the Clinique blue stuff.
Then I went and bought another bottle of the Clinique blue stuff.
ETA–make sure to compare the # of ounces of product when comparing prices. I think the other brands come in smaller bottles. But you might not wear makeup often enough for that to be a consideration.
I’m not surprised the first post endorsed the Body Shop Chamomile. That’s what I came in to say; it’s fantastic stuff. Very gentle, not greasy, not as expensive as Clinique. And it gets pot resin off of fingers really easily (don’t ask how I know).
AlMay makes two kinds of eye makeup remover–I like the "Non Oily"variety.
I go to the CVS and get a bottle of glycerin (4 oz. = $2-3) Then I fill the old Almay bottle about 1/4 glycerin and 3/4 water. Put the squirty top back on and shake well before using.
The one thing to be careful of is if you don’t use it very often. Glycerin is a good food for bacteria, so in your case you may want to keep it in the fridge between uses, and wash the bottle well before refilling.
A bottle of glycerin will make about 756 bottles of makeup remover. (well, approximately) But it usually gets used up before that because I also combine it with sesame oil and bergamot for a skin lotion.
Vaseline. I don’t find the grease stays. Smear it on, wipe it off with a tissue and all the grease goes with it - no residue.
Cheap, and I find it softens the skin in the eye area in a pleasant way.
Cold Cream leaves my skin feeling soft and clean, not greasy. That’s why I recommended it. I’ve used eye makeup removers that were greasy feeling and hated them.
Baby wipes do a great job. Even waterproof mascara comes right off, and they’re gentle and non-irritating. Plus, easily portable and cheap. (I wear contact lenses, so I’m cautious about what I use around my eyes, but even the cheap baby wipes work great for me.)
If you have a Target near you, their Sonia Kashuk brand is THE BEST. And it’s only $10!! I’ve converted dozens of friends onto it.
You know those Olay makeup remover cloths, that are wet? Get those generic - walmart, target, cvs, whatever. If you like 'em (probably $4 for a 30 pack or so), get a bigger box, or at Costco, Sam’s, etc.
They combine the best of both worlds - they have stuff in them that takes makeup (even big eye makeup) off easily, but they’re not super saturated (like a washcloth or wetted cotton ball is) so it won’t get in your eyes.
Based on what you said about being a litle klutzy (nothing to be ashamed of, I am!) and wanting something cheap but effective, this is probably your best bet.
Definitely don’t do what **Lo-Slung Denim **suggests. It works well, but Vaseline is very greasy, and doing this can give you milia, those little white pseudo-zits around your eyes.