First of all I completely feel where you are coming from. Your gear is only part of your music-making but if it is off or you aren't into the sounds, it can take some of the fun out of playing guitar. As a gearhead even from a young age there has always been (and still is) a good chunk of gear I either couldn't or shouldn't buy. That said I hope to have a few practical tips here that are either free or cheap that can help you find a new tone or flavor. I've ordered them from free to less cheap:
Free: Adjust your pickup height. The screws on the right and left of the pickup raise (clockwise) or lower (counterclockwise) your pickup. Higher leads to more output and a more compressed tone, up to a point at which you can get a slightly distorted tone and have issues with string pull. I'm going to write up a whole post on this and will link to it later, but don't be afraid to adjust these screws. Also you can tilt a pickup towards or away from the high/low strings to give it a brighter/darker flavor when playing chords. Worth noting that this is all completely reversible.
Free: Adjust individual pickup screw heights. If you have a humbucker or a (typically non-Strat/Tele) pickup with screws on individual pole pieces, you can adjust these up (counterclockwise) or down (clockwise). This is used for two main purposes: 1) to balance the output of strings by matching (more or less) the radius of the pickup poles to the radius of your bridge (look at it from the side - your bridge has a curve to it like your fretboard), and 2) setting individual string outputs to match your personal flavor. On one of my guitars I was getting a weaker high E string - likely because the string was just a bit off the pole piece (Gibson spaced pickup with Fender spaced bridge). So I just cranked up the pole piece a hair and I had the tone I was looking for. Go too high and you may find yourself touching the string to the pickup pole, which can make a "clicking" noise - watch for that. Note: Do this after you make your "macro" pickup adjustment in step 1. This is also completely reversible.
Free: Adjust the tone/gain/volume knobs on your amp. I didn't put this first as it seems so obvious, but I think sometimes it is easy to get stuck in the rut of what "should be right". I mean, if it doesn't sound good at 5-5-5 (bass-mid-treble) it's not going to sound good right? Well, not really. I thought that way until I bought a Mesa Mark V head. There are a lot of great tones in that amp, but you really have to be willing to use "the whole knob" on the tone/level/drive settings to get them. Bass at 1/10? I've been there, and it sounded good! Don't be afraid to try extreme settings - if they sound good to you who cares where the knobs are? Try 1-1-1, 10-10-10, and all other manner of combinations - these are complicated analog circuits, not perfect digital circuits - sometimes funky combinations work.
Free: Adjust the volume and tone knobs on your guitar. Many guitarists (myself included) tend to leave these at "10" and not mess with them much. There is some good reason to do this on a passive guitar (as even your volume knob can roll off high frequencies, you get the clearest/brightest/loudest sound this way) but there are interesting tones to be had from changing these. As an example, Clapton's classic "Woman" tone was achieved with the guitar's tone knob at around "1". Also, if you can make on-the-fly adjustments you can use the volume/tone knobs to help with phrasing/expression. Some amps also just need higher or lower input levels. I have a handmade amp where the front end was lifted from an old Fender Harvard amp. This amp front-end overdrives (not elegantly) with anything hotter than a vintage single coil. For my humbucker-equipped guitars not to sound "farty", I have to turn back the volume on the guitar a lot.
Free: Check and fix the intonation on your guitar. For your guitar to sound right its intonation needs to be set. What that means is that, as an example, an open high E and the fretted 12th fret octave E on your guitar would both be in tune with each other. For various reasons, this is not always the case (intonation was never set at the factory, the wood moved a bit, the truss rod was adjusted, the action is higher/lower, etc.). The easiest way to visualize this is that the 12th fret should fall directly in between the nut and the bridge of your guitar - if the bridge say was too far back, the 12th fret would no longer be in the center, and so the open and octave notes would no longer be in tune with each other. This makes your playing sound dissonant/out of tune, either with yourself (if playing chords or fast riffs) or with your band. How to do it? Check out Sweetwater's tutorial HERE.
Cheap: Change your strings. If you haven't changed your strings in months, it is worth the $5-8 to do so. Older strings lose some of their high frequency sparkle over time and sound more "dead". In addition, they won't intonate properly (see last suggestion regarding guitar intonation).
Another variant of change your strings is to change your string type. Now, I'm not talking about changing the gauge (e.g. 9s vs 10s vs 11s) - that changes how much pull (force) there is on the guitar, and you would potentially need a new setup (truss rod adjustment, potentially re-filed nut). But if you wanted say a mellower/more vintage tone, using your current string gauge try pure nickel strings. If you want a higher output/more aggressive sound, try one of the new more-magnetic strings in your gauge like the Ernie Ball Cobalt's HERE.
Cheap: Change your guitar's tone or volume pot values. This is only relevant if you have 250K or 500K pots and you wish you had more output/high frequency tone. In that case you could swap them for 500K or 1M pots, which will give you a hair more output and a hair more HF. If you can't make this mod yourself it won't be that cheap as you'll have to pay someone to do it, but if you are willing to alter your own guitar you can do this for <$10. Why not go from 500K to 250K? Well because you can get that same sound without changing the pot by just turning the nob to 9-9.5 or so.
Cheap: Change the value of the capacitor in your guitar's tone circuit. This will only have an effect if you currently use the tone knob on your guitar - if you don't you won't notice a difference at "10" on the tone control. What this does is it actually changes the shape of the guitar's frequency response curve when the tone control is in use - larger value capacitors will bleed off more of your mids/highs as they are engaged and smaller value capacitors will confine their effects to higher frequencies. Along the lines of changing your guitar's pots this is only cheap if you are confident enough to do it yourself. I would really only say this mod is for a player who plays with the tone control engaged a lot and feels that tone-control-engaged tone needs tweaking.
Cheap: Try a new pick thickness/type. This is really reaching, but it is cheap to try. My guess is that you'll want to stick to the thickness/type you like, but thicker/thinner picks do give different attacks, and even material makes a difference (my 1mm Tortex and Pickboy Graphite do sound slightly different).
Somewhat cheap: Change your guitar cable. If you were using a very long, very old, or very very cheap cable (think big box store unbranded ones), then I'd recommend buying one nicer, shorter length cable. A decent 6 ft cable should run you $20 or less. I cannot guarantee you'll hear a difference (unless your cable was very very long and your guitar is passive, in which case I can guarantee it), but good cables last a long time and, especially if you are looking for better clarity, this is a good one to check off. If you can only afford one good cable and you have multiple runs, put your best cable from your guitar to your first buffer/buffered pedal.
Moderately expensive: There's always used pickups. People like me will try a set for a while and, if they aren't what they hoped for, sell their old pickups used on eBay. Note that apart from a slight chance the potting/wires will have loosened, making the pickup more microphonic, and the slight demagnetization that occurs over time (slight, and some people prefer this) these pickups should be fine for your use. Just make sure they have enough lead (wire) length left, or that you are comfortable soldering a new wire onto the old wire and either heat wrapping the joint or covering it in electrical tape. Also ask for a picture of the pickup face - this is where most of the cosmetic wear will occur, so best to know what you're getting before it arrives. If you are worried, email and ask the seller if there are any known issues with the pickup. Most people are honest and they will tell you what is wrong even if they omitted it originally from the posting. There are no risk-free used transactions, but usually you get a great deal and things work out.
I hope that's helpful and good luck! Do let me know if you have another ideas and I'll post them here, or just add them to the comments.